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2015年高考数学人教A版,理)一轮复习配套讲义:第10篇 第1讲 分类加法计数原理与分步乘法计数原理_图文

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confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in differ ent areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o to learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w ork; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programm es and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

第 1 讲 分类加法计数原理与分步乘法计数原理 [最新考纲] 1.理解分类加法计数原理和分步乘法计数原理. 2.会用分类加法计数原理或分步乘法计数原理分析和解决一些简单的实际问题.

知识梳理 1.分类加法计数原理 完成一件事有 n 类不同的方案,在第一类方案中有 m1 种不同的方法,在第二类 方案中有 m2 种不同的方法,……,在第 n 类方案中有 mn 种不同的方法,则完成 这件事情,共有 N=m1+m2+…+mn 种不同的方法. 2.分步乘法计数原理 完成一件事情需要分成 n 个不同的步骤,完成第一步有 m1 种不同的方法,完成 第二步有 m2 种不同的方法,……,完成第 n 步有 mn 种不同的方法,那么完成这 件事情共有 N=m1×m2×…×mn 种不同的方法. 3.分类加法计数原理与分步乘法计数原理,都涉及完成一件事情的不同方法的 种数.它们的区别在于:分类加法计数原理与分类有关,各种方法相互独立,用 其中的任一种方法都可以完成这件事;分步乘法计数原理与分步有关,各个步骤 相互依存,只有各个步骤都完成了,这件事才算完成.
辨析感悟 1.两个计数原理的理解 (1)在分类加法计数原理中,两类不同方案中的方法可以相同.(×) (2)在分类加法计数原理中,每类方案中的方法都能直接完成这件事.(√) (3)在分步乘法计数原理中,每个步骤中完成这个步骤的方法是各不相同的.(√) (4)在分步乘法计数原理中,事情是分两步完成的,其中任何一个单独的步骤都 能完成这件事.(×) 2.两个计数原理的应用 (5)(教材习题改编)三个人踢毽,互相传递,每人每次只能踢一下,由甲开始踢, 经过 5 次传递后,毽又被踢回给甲,则不同的传递方式共有 10 种.(√) (6)用数字 2,3 组成四位数,且数字 2,3 至少都出现一次,这样的四位数共有 14

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level lim ited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dministeri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he constructi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nt s two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence, e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s ho uld have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o t o learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w or k; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

个.(√) [感悟·提升] 1.两点区别 一是分类加法计数原理中,完成一件事的方法属于其中一类并且只属于其中一 类,简单的说分类的标准是“不重不漏,一步完成”,如(1)、(2). 二是分步乘法计数原理中,各个步骤相互依存,在各个步骤中任取一种方法,即 是完成这个步骤的一种方法,简单的说步与步之间的方法“相互独立,分步完 成”,如(3)、(4). 2.两点提醒 一是分类时,标准要明确,应做到不重不漏;可借助几何直观,探索规律,如(5). 二是分步时,要合理设计顺序、步骤,并注意元素是否可以重复选取,如(6)中 2,3 可重复但至少各出现一次.
学生用书 第 172 页

考点一 分类加法计数原理 【例 1】 (2013·福建卷改编)满足 a,b∈{-1,0,1,2},且关于 x 的方程 ax2+2x+ b=0 有实数解的有序数对(a,b)的个数为( ). A.14 B.13 C.12 D.9 解析 由于 a,b∈{-1,0,1,2}. (1)当 a=0 时,有 x=-b2为实根,则 b=-1,0,1,2 有 4 种可能; (2)当 a≠0 时,则方程有实根, ∴Δ=4-4ab≥0,所以 ab≤1.(*)
①当 a=-1 时,满足(*)式的 b=-1,0,1,2 有 4 种. ②当 a=1 时,b=-1,0,1,有 3 种可能.

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dm inisteri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he con structi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence , e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o to learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w ork; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advan cing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of cal ls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on m asse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situa ti on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maver i ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

③当 a=2 时,b=-1,0,有 2 种可能.

∴由分类加法计数原理,有序数对(a,b)共有 4+4+3+2=13(个). 答案 B 规律方法 分类标准是运用分类计数原理的难点所在,重点在于抓住题目中的关

键词或关键元素、关键位置.首先根据题目特点恰当选择一个分类标准;其次分

类时应注意完成这件事情的任何一种方法必须属于某一类. 【训练 1】 某同学有同样的画册 2 本,同样的集邮册 3 本,从中取出 4 本赠送 给 4 位朋友,每位朋友 1 本,则不同的赠送方法共有( ). A.4 种 B.10 种 C.18 种 D.20 种 解析 赠送一本画册,3 本集邮册,需从 4 人中选取一人赠送画册,其余送邮册,

有 C14种方法.

赠送 2 本画册,2 本集邮册,只需从 4 人中选出 2 人送画册,其余 2 人送邮册,

有 C24种方法.

由分类加法计数原理,不同的赠送方法有 C14+C24=10(种).

答案 B

考点二 分步乘法计数原理

【例 2】 将字母 a,a,b,b,c,c 排成三行两列,要求每行的字母互不相同, 每列的字母也互不相同,则不同的排列方法共有( ). A.12 种 B.18 种 C.24 种 D.36 种

解析 先排第一列,由于每列的字母互不相同,因此共有 A33种不同排法.再排

第二列,其中第二列第一行的字母共有 2 种不同的排法,第二列第二、三行的字

母只有 1 种排法.因此共有 A33·2·1=12(种)不同的排列方法. 答案 A 规律方法 (1)利用分步乘法计数原理解决问题要按事件发生的过程合理分步,即

分步是有先后顺序的,并且分步必须满足:完成一件事的各个步骤是相互依存的,

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party 's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dministeri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he constructi on of learni ng -oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence, e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o t o learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w or k; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

只有各个步骤都完成了,才算完成这件事. (2)分步必须满足两个条件:一是步骤互相独立,互不干扰;二是步与步确保连
续,逐步完成. 【训练 2】 将一个四面体 ABCD 的六条棱上涂上红、黄、白三种颜色,要求共 端点的棱不能涂相同颜色,则不同的涂色方案有( ). A.1 种 B.3 种 C.6 种 D.9 种 解析 因为只有三种颜色,又要涂六条棱,所以应该将四面体的对棱涂成相同的 颜色.故有 3×2×1=6 种涂色方案. 答案 C
考点三 两个计数原理的综合应用 【例 3】 (2014·济南质检)如图,用 4 种不同的颜色对图中 5 个区域涂色(4 种颜 色全部使用),要求每个区域涂一种颜色,相邻的区域不能涂相同的颜色,则不 同的涂色种数有________.
1 2 45 3 审题路线 由于区域 1,2,3 与区域 4 相邻,由条件宜采用分步处理,又相邻区域 不同色,因此应按区域 1 和区域 3 是否同色分类求解. 解析 按区域 1 与 3 是否同色分类;
(1)区域 1 与 3 同色;先涂区域 1 与 3 有 4 种方法,再涂区域 2,4,5(还有 3 种颜色) 有 A33种方法. ∴区域 1 与 3 涂同色,共有 4A33=24 种方法. (2)区域 1 与 3 不同色:先涂区域 1 与 3 有 A24种方法,第二步涂区域 2 有 2 种涂 色方法,第三步涂区域 4 只有一种方法,第四步涂区域 5 有 3 种方法. ∴这时共有 A42×2×1×3=72 种方法,

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e furthe r dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dm inisteri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he con structi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence , e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould hav e "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o to learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w ork; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advan cing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, fee l they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situa ti on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maver i ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

故由分类加法计数原理,不同的涂色种数为 24+72=96. 答案 96 规律方法 (1)解决涂色问题,一定要分清所给的颜色是否用完,并选择恰当的涂 色顺序. (2)切实选择好分类标准,分清哪些可以同色,哪些不同色. 【训练 3】 如果一个三位正整数如“a1a2a3”满足 a1<a2,且 a2>a3,则称这样的三 位数为凸数(如 120,343,275 等),那么所有凸数的个数为( ). A.240 B.204 C.729 D.920 解析 若 a2=2,则“凸数”为 120 与 121,共 1×2=2 个.若 a2=3,则“凸数” 有 2×3=6 个.若 a2=4,满足条件的“凸数”有 3×4=12 个,…,若 a2=9, 满足条件的“凸数”有 8×9=72 个.∴所有凸数有 2+6+12+20+30+42+56 +72=240(个). 答案 A

1.分类加法计数原理与分步乘法计数原理是解决排列组合问题的基础并贯穿始 终.(1)分类加法计数原理中,完成一件事的方法属于其中一类并且只属于其中 一类.(2)分步乘法计数原理中,各个步骤相互依存,步与步之间的方法“相互 独立,分步完成”. 2.(1)切实理解“完成一件事”的含义,以确定需要分类还是需要分步进行.(2) 分类的关键在于要做到“不重不漏”,分步的关键在于要正确设计分步的程序, 即合理分类,准确分步. 3.若综合利用两个计数原理,一般先分类再分步.
学生用书 第 173 页

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party 's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dministeri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he constructi on of learni ng -oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence, e nha nce s elf -aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o t o learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w or k; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

创新突破 9——与计数原理有关的新定义问题 【典例】 (2012·湖北卷)回文数是指从左到右与从右到左读都一样的正整数.如 22,121,3 443,94 249 等.显然 2 位回文数有 9 个:11,22,33,…,99.3 位回文数有 90 个:101,111,121,…,191,202,…,999.(*) 则:(1)4 位回文数有________个; (2)2n+1(n∈N*)位回文数有________个.(**) 突破:由(*)式,理解“特殊”背景——回文数的含义,借助计数原理计算. 结合(**),可从 2 位回文数,3 位回文数,4 位回文数探索求解方法,从特殊到 一般发现规律. 解析 (1)4 位回文数相当于填 4 个方格,首尾相同,且不为 0,共 9 种填法;中 间两位一样,有 10 种填法. 共计 9×10=90(种)填法,即 4 位回文数有 90 个. (2)根据回文数的定义,此问题也可以转化成填方格. 由计数原理,共有 9×10n 种填空. 答案 (1)90 (2)9×10n [反思感悟] (1)一题两问,以“回文数”为新背景,考查计数原理,体现了化归思 想,将确定回文数的问题转化为“填方格”问题,进而利用分步乘法计数原理解 决,将新信息转化为所学的数学知识来解决. (2)从特殊情形入手,通过分析、归纳,发现问题中隐含的一些本质特征和规律, 然后再推广到一般情形,必要时可以多列举一些特殊情形,使规律方法更加明确. 【自主体验】 1.(2014·扬州调研)从 8 名女生 4 名男生中,选出 3 名学生组成课外小组,如果 按性别比例分层抽样,则不同的抽取方法数为________种. 解析 从男生中抽取 1 人有 4 种方法. 从女生中抽取两人,有 C28=28 种方法.

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e furthe r dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dm inisteri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he con structi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence , e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould hav e "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o to learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w ork; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advan cing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, fee l they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situa ti on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maver i ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

∴由分步乘法计数原理,共有 28×4=112 种方法. 答案 112 2.(2013·山东卷改编)用 0,1,…,9 十个数字,可以组成有重复数字的三位数的 个数为( ). A.243 B.252 C.261 D.648 解析 0,1,2,…,9 共能组成 9×10×10=900(个)三位数,其中无重复数字的三
位数有 9×9×8=648(个),∴有重复数字的三位数有 900-648=252(个). 答案 B

对应学生用书 P357 基础巩固题组
(建议用时:40 分钟)
一、选择题 1.某市汽车牌照号码可以上网自编,但规定从左到右第二个号码只能从字母 B, C,D 中选择,其他四个号码可以从 0~9 这十个数字中选择(数字可以重复),有 车主第一个号码(从左到右)只想在数字 3,5,6,8,9 中选择,其他号码只想在 1,3,6,9 中选择,则他的车牌号码可选的所有可能情况有( ). A.180 种 B.360 种 C.720 种 D.960 种 解析 按照车主的要求,从左到右第一个号码有 5 种选法,第二位号码有 3 种选 法,其余三位号码各有 4 种选法.因此车牌号码可选的所有可能情况有 5×3×4×4×4=960(种). 答案 D 2.(2012·新课标全国卷)将 2 名教师,4 名学生分成 2 个小组,分别安排到甲、 乙两地参加社会实践活动,每个小组由 1 名教师和 2 名学生组成,不同的安排方 案共有( ).

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party 's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dministeri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he constructi on of learni ng -oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence, e nha nce s elf -aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o t o learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w or k; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

A.12 种 B.10 种 C.9 种 D.8 种 解析 分两步:第一步,选派一名教师到甲地,另一名到乙地,共有 C12=2 种选
派方法;
第二步,选派两名学生到甲地,另外两名到乙地,共有 C24=6 种选派方法. 由分步乘法计数原理,不同选派方案共有 2×6=12(种). 答案 A 3.6 位选手依次演讲,其中选手甲不在第一个也不在最后一个演讲,则不同的 演讲次序共有( ). A.240 种 B.360 种 C.480 种 D.720 种 解析 第一步先排甲,共有 A41种不同的排法;第二步再排其他人,共有 A55种不
同的排法.因此不同的演讲次序共有 A41·A55=480(种). 答案 C 4.从集合{1,2,3,…,10}中任意选出三个不同的数,使这三个数成等比数列, 这样的等比数列的个数为( ). A.3 B.4 C.6 D.8 解析 以 1 为首项的等比数列为 1,2,4;1,3,9;
以 2 为首项的等比数列为 2,4,8;
以 4 为首项的等比数列为 4,6,9;
把这四个数列顺序颠倒,又得到 4 个数列,
∴所求的数列共有 2(2+1+1)=8(个). 答案 D 5.集合 P={x,1},Q={y,1,2},其中 x,y∈{1,2,3,…,9},且 P?Q.把满足上 述条件的一对有序整数对(x,y)作为一个点的坐标,则这样的点的个数是( ). A.9 B.14 C.15 D.21 解析 当 x=2 时,x≠y,点的个数为 1×7=7(个). 当 x≠2 时,由 P?Q,∴x=y.

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e furthe r dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dm inisteri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he con structi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence , e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould hav e "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o to learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w ork; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advan cing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, fee l they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situa ti on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maver i ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

∴x 可从 3,4,5,6,7,8,9 中取,有 7 种方法.
因此满足条件的点共有 7+7=14(个). 答案 B 二、填空题 6.从班委会 5 名成员中选出 3 名,分别担任班级学习委员、文娱委员与体育委 员,其中甲、乙二人不能担任文娱委员,则不同的选法共有________种(用数字 作答). 解析 第一步,先选出文娱委员,因为甲、乙不能担任,所以从剩下的 3 人中选
1 人当文娱委员,有 3 种选法.
第二步,从剩下的 4 人中选学习委员和体育委员,又可分两步进行:先选学习委
员有 4 种选法,再选体育委员有 3 种选法. 由分步乘法计数原理可得,不同的选法共有 3×4×3=36(种). 答案 3 7.如图所示,在连接正八边形的三个顶点而成的三角形中,与正八边形有公共 边的三角形有________个. 解析 把与正八边形有公共边的三角形分为两类: 第一类,有一条公共边的三角形共有 8×4=32 个;
第二类,有两条公共边的三角形共有 8 个.
由分类加法计数原理知,共有 32+8=40(个). 答案 40 8.8 名世界网球顶级选手在上海大师赛上分成两组,每组各 4 人,分别进行单 循环赛,每组决出前两名,再由每组的第一名与另一组的第二名进行淘汰赛,获 胜者角逐冠、亚军,败者角逐第 3,4 名,大师赛共有________场比赛. 解析 小组赛共有 2C24场比赛;半决赛和决赛共有 2+2=4 场比赛;根据分类加 法计数原理共有 2C24+4=16(场)比赛. 答案 16

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party 's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dministeri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he constructi on of learni ng -oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence, e nha nce s elf -aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o t o learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w or k; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

三、解答题

9.电视台在“欢乐在今宵”节目中拿出两个信箱,其中放着竞猜中成绩优秀的

观众来信,甲箱中有 30 封,乙箱中有 20 封,现由主持人抽奖确定幸运观众,若

先从中确定一名幸运之星,再从两箱中各确定一名幸运观众,有多少种不同结

果?

解 (1)幸运之星在甲箱中抽,选定幸运之星,再在两箱内各抽一名幸运观众有

30×29×20=17 400 种.

(2)幸运之星在乙箱中抽取,有 20×19×30=11 400 种.

共有不同结果 17 400+11 400=28 800(种).

10.“渐升数”是指每个数字比它左边的数字大的正整数(如 1 458),若把四位

“渐升数”按从

小到大的顺序排列,求第 30 个“渐升

数”.

1 2 ××

解 渐升数由小到大排列,形如的渐升数共有 6+5+4+3+2+1=21(个).

1 3 4 × 形如的渐升数共有 5 个.
形如 1 3 5 × 的渐升数共有 4 个.

故此时共有 21+5+4=30(个).

因此从小到大的渐升数的第 30 个必为 1 359.

能力提升题组

(建议用时:25 分钟)

一、选择题 1.如图,一环形花坛分成 A,B,C,D 四块,现有 4 种不同的花供选种, 要求在每块里种 1 种花,且相邻的 2 块种不同的花,则不同的种法总数为( ). A.96 B.84 C.60 D.48 解析 可依次种 A,B,C,D 四块,当 C 与 A 种同一种花时,有 4×3×1×3=
36 种种法;当 C 与 A 所种花不同时,有 4×3×2×2=48 种种法.
由分类加法计数原理,不同的种法种数为 36+48=84. 答案 B

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e furthe r dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dm inisteri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he con structi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence , e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould hav e "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o to learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w ork; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advan cing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, fee l they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situa ti on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maver i ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

2.在某种信息传输过程中,用 4 个数字的一个排列(数字允许重复)表示一个信 息,不同排列表示不同信息.若所用数字只有 0 和 1,则与信息 0110 至多有两 个对应位置上的数字相同的信息个数为( ). A.10 B.11 C.12 D.15 解析 若 4 个位置的数字都不同的信息个数为 1;若恰有 3 个位置的数字不同的
信息个数为 C34;若恰有 2 个位置上的数字不同的信息个数为 C24.
由分类加法计数原理知满足条件的信息个数为 1+C34+C24=11. 答案 B 二、填空题 3.如图所示,在 A、B 间有四个焊接点,若焊接点脱落,则可能导致电路不通, 今发现 A、B 之间线路不通,则焊接点脱落的不同情况有________种.

解析 四个焊点共有 24 种情况,其中使线路通的情况有:1、4 都通,2 和 3 至
少有一个通时线路才通共有 3 种可能.故不通的情况有 24-3=13(种)可能. 答案 13 三、解答题 4.用 n 种不同颜色为下列两块广告牌着色(如图所示),要求在 A,B,C,D 四 个区域中相邻(有公共边的)区域不用同一种颜色.

(1)若 n=6,为①着色时共有多少种不同的方法? (2)若为②着色时共有 120 种不同的方法,求 n. 解 (1)分四步:第 1 步涂 A 有 6 种不同的方法,第 2 步涂 B 有 5 种不同的方法, 第 3 步涂 C 有 4 种不同的方法,第 4 步涂 D 有 4 种不同的方法. 根据分步乘法计数原理,共有 6×5×4×4=480 种不同的方法. (2)由题意,得 n(n-1)(n-2)(n-3)=120,注意到 n∈N*,可得 n=5.

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e further dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party 's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dministeri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he constructi on of learni ng -oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence, e nha nce s elf -aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould have "com mon lang uage" socialist countries must have "unity of will". History ha s

confere nces , learne d s uperi ors polici es; re ports, y ou can lear n to deal with problems, art, j ust wante d to lear n, to lear n at any time. To continuously expand the s cope of the study. T he complexity and comprehensiv enes s of our work, deci de d to not only do w e want to be "profess ionals", or if "generalists", to dabble in different areas of knowle dge. Mastery of knowl edge not only to have k now ledge to rati onal a nalysis . Thi s on requirements we , not only to l earni ng national of route, a nd a pproa ch, and policy, als o t o learning nati onal of legal, and regulati ons; not only to with politi cal the or y armed mind, al so to w ith economic t heory g uide w or k; not only to read histor y, als o to rea d hist ory; not only t o absorpti on SM of mirror, als o to gets i s of road; not only t o from local le arn, al so to t o out side le arn; not only to to books lear n, als o to field study le arn.

Therefore, I woul d encourage you, and more to t he outside worl d whe n I have time to take a look at, take a stroll, outsi de dev elopments,

learn other pe ople' s devel opme nt appr oach, a nd then come ba ck to gui de our work . Second, we must t hink. "Learni ng without thoug ht to overs hadow, t hinki ng without lear ning is peril ous." We want to foster the character of advancing wit h the times, forge a head, often reflect themselves i n ada pting to the new s ituation on whet her ther e are delays , have anyt hing to fear in t he reform and innovation, whether i n terms of accelerating the devel opme nt of a relaxation, kee p pr omising State of mind. In order t o do i nvestigations, inve stigations is the r oad to heaven, God di sposes of the ba se . To wa nts to real heard trut h, and justi ce to tr uth, a nd get truth, receive d effectivene ss, on must i n-dept h act ual, and outreach, and in -de pth mas ses, w orshi p masse s for Divisi on, a nd mas ses heart, with mas ses wit h dis cussi on every one care of problem, liste ning t hey of calls , understa nd they of mood, feel they of suffering, summary they of experi ence, concentrated t hey of wis dom, e spe cially on masse s most

hope, and most urgent, and most w orries, a nd m ost complai ned of hot, a nd difficulties a nd focus problem, more to active rese arch, caug ht not put. Dare to i nnovate, in our work , often remai n "the ol d way doesn't w ork, the new a ppr oach would not" situati on, t he reas on, t he key is that ma ny pe ople k now t hat copying other people's i deas, me cha nically, using some one e lse's old way s. To change t his pre dicame nt, requires us to break the s ha ckles of traditi onal conce pts to overcome conservative, conformist, good at findi ng ne w problems a nd t o accept new thi ngs, s ummarize new experie nce, new i deas, developing new programmes and Maveri ck, a ne w approa ch to solve probl ems, s pee d up devel opment . Especially i n impleme nt superior poli cy s pirit of proces s in the, both impl ementation, and ca nnot mechani cally, t o to extraordi nary of courage a nd develop enter prisi ng of s pirit, put flexibility a nd principl e com bine d up, put superi or of spirit a nd l ocal real ity com bine d up, Yong conspira cy t o

breakthrough of poli cy, a nd exerci se innovation of lift, develope d out development w orks of, and gras s-r oots wel come s of, and

学生用书 第 173 页

Accor ding to Office Party of mass line education pra ctice a ctivities le d group of unified arrangements , units main le d to for ca dres w orkers Shang a times party lect ure, due to himself level limited, only put t his stage conce ntrated lear ning of ex perience today and everyone common with lear ning exchange, pur pose is let w e furthe r dee p understa ndi ng mass li ne of connotati on, i nsiste d party of mas s line, do ma sses w ork, foll owing mai n from four a as pe cts tol d: a, a nd full awarene ss party of mass line educati on practice activities of major mea ning Party's 18 major disti nct pr opose d to focus on the party's adva nce d nat ure and purity, i n the party, with "pragmatic a nd clea n for the people" as the main conte nt of the party's mass li ne a nd e ducational pra ctice.

This is comrade XI Ji npi ng as party General Secretary a nd a dher e to strictly a dm inisteri ng the party, strengthe n the party's major de cisi on i s in li ne wit h the public expectations a nd strengthe ning t he con structi on of learni ng-oriente d

service i nnovation of Marxist party's major de ployment, i s the important meas ure to adva nce t he great ca use of s ocia lism with Chi nese characteri stics . First, carry out the party's mass li ne i n education pra ctice, wa s carryi ng 18 of the party spir it, summon a powerful force for realizing t he great rej uvenation of the Chi nese nation the Chinese dre am of urgent ne eds . Party's 18 t o promote strategic de ployme nt to buildi ng sociali sm with Chine se characteristi cs, prese nts two 10 0-year g oal, namel y, by 2 020 China' s gross domesti c pr oduct and per capita i ncome of ur ban a nd rural re side nts in 2 0 10 on t he ba sis of double complete the buildi ng of a well -off society; the mi ddle of this century i nto a pr os perous, democrati c, civi lized a nd harmoni ous Socialist modern country, a nd on t his ba sis, the Chines e dream of realizi ng the great rej uvenati on of the Chi nese nation. 18 Congress of the part y, Comrade XI Ji npi ng repeate dly expounded t he Chine se dream. T he ba sic connotation of the Chines e dream, is t he

national prosperit y, nati onal revitalizati on, t he ha ppi nes s of the pe opl e, China important to foll ow is to kee p China Roa d, carry forwar d the s pirit and cohesi on stre ngth of China , dream dreams of the pe opl e of Chi na, but determi ned confidence , e nha nce s elf-aware ness, a chi eve self-relia nce, to bui ld a stronger Chi na, civi lization, harm ony, bea uty, China , Chi na, China.

Strategic conce ption of China wa s 18 the spirit of the e nrichment a nd development of the party, conscie ntiously st udy the Chi nese dream, leadi ng pe ople t o hard t o realize the Chi nese dream, mass e ducation a ctivities i n depth t he fundamental starti ng point and ending poi nt. Strengthe n the e ducation of the party's mas s line , hel ps to train t he collective consci ousne ss of the unity of the party and the people, playi ng the Chine se dream i deol ogical base s. Comrade Ma o Zedong stress ed that parties s hould hav e "com mon lang uage" socialist countries must have "unity of will". History ha s



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