高中数学 第一章 计数原理 1.3 组合 1.3.1 组合与组合数公式课件 北师大版选修23

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1、3 3组组合合第1 1课时组合与组合数公式目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1.理解组合的

2、意义,能写出一些简单问题的组合.2.能够正确认识排列与组合的区别.3.掌握组合数公式,能用组合数公式及其性质进行计算、化简.4.能利用组合数公式解简单的组合问题.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳

3、理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123451.一般地,从n个不同的元素中,任取m(mn)个元素为一组,叫作从n个不同元素中取出m个元素的一个组合,我们把有关求组合的个数的问题叫作组合问题.说明:(1)组合的概念中有两个要点:取出元素,且要求n个元素是不同的;“只取不排”,即取出的m个元素与顺序无关,无序性是组合的特征性质.(2) 只要两个组合中的元素完全相同,那么不管元素的顺序如何,都是相同的组合.当两个组合中的元素不完全相同(即使只有一个元素不同),就是不同的组合.(3)组合与排列的共同点:从n个不同的元素中任取m个元

4、素;不同点:对于排列,取出元素后还需对所取出的元素进行排列,即对顺序有要求,而组合对取出的元素无需排列,只需组成一组即可,对顺序无要求.可总结为:有序排列,无序组合.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知

5、识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345【做一做1】 给出下面几个问题,其中是组合问题的有()由1,2,3,4构成的含有2个元素的集合个数;五个队进行单循环比赛的比赛场次数;由1,2,3组成两位数的不同方法数;由1,2,3组成的无重复数字的两位数的个数.A.B.C.D.答案:C目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航D

6、IANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYA

7、NLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳

8、理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUI

9、TANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理12345目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISH

10、ULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三【例1】 判断下列问题是组合问题还是排列问题.(1)设集合A=a,b,c,d,则集合A的含有3个元素的子集有多少个?(2)一个班中有52人,任意两个人握一次手,共握多少次手?(3)4个人去干5种不同的工作,每人干一种,有多少种分工方法?分析:交换任何两个元素的顺序,看结果有无影响,如无影响则是组合问题.解:(1)因为集合中取出的元素具有“无序性”,所以这是组合问题;(2)因为两人握手是相互的,没有顺序之分,所以这是组合问题;(3)因为5种工作是不同的, 从5种

11、不同的工作中选出4种,按一定的顺序分配给4个人,它与顺序有关,所以这是排列问题.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHI

12、SHISHULI知识梳理题型一题型二题型三反思区分一个问题是排列问题还是组合问题,关键是看它有无“顺序”,有顺序就是排列问题,无顺序就是组合问题.要判定它是否有顺序的方法是:先将元素取出来,看交换元素的顺序对结果有无影响,有影响就是“有序”,也就是排列问题;没有影响就是“无序”,也就是组合问题.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演

13、练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三【变式训练1】 判断下列各事件是排列问题还是组合问题,并求出相应的排列数或组合数.(1)10人相互通一次电话,共通多少次电话?(2)10个球队以单循环进行比赛(每两队比赛一次),共进行多少场次?(3)从10个人中选出3个作为代表去开会,有多少种选法?(4)从10个人中选出3个担任不同学科的课代表,有多少种选法?分析:解答本题主要是分清取出的

14、这m个(2个或3个)元素是进行排列还是组合,即确定其与顺序有关还是无关.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHIS

15、HULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三目标

16、导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知

17、识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析

18、随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演

19、练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUX

20、I典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三【例3】 在一次数学竞赛中,某学校有12人通过了初试,学校要从中选出5人参加市级培训.在下列条件下,有多少种不同的选法?(1)任意选5人;(2)甲、乙、丙三人必须参加;(3)甲、乙、丙三人不能参

21、加;(4)甲、乙、丙三人只能有1人参加.分析:利用组合数公式与分步计数原理解答.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHI

22、SHISHULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题

23、型三反思解答简单的组合问题的步骤:(1)弄清要做的这件事是什么事;(2)选出的元素是否与顺序有关,也就是看看是不是组合问题;(3)结合两计数原理利用组合数公式求出结果.目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI

24、知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三【变式训练3】 现有10名教师,其中男教师6名,女教师4名.(1)现要从中选2名教师去参加会议,有多少种不同的选法?(2)选出2名男教师或2名女教师去外地学习的选法有多少种?(3)现要从中选出男、女教师各2名去参加会议,有多少种不同的选法?目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳

25、理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理题型一题型二题型三目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透

26、析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1234561.从5名同学中推选4人去参加一个会议,不同的推选方法总数是()A.10B.5C.4D.1答案:B目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI

27、SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123456A.36B.84C.88 D.504答案:B目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI

28、SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1234563.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()A.12种 B.10种C.9种D.8种解析:先安排1名教师和2名学生到甲地,再将剩下的1名教师和2名答案:A目标导航知识梳理典

29、例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123456目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演

30、练知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理123456目标导航知识梳理典例透析随堂演练目标导航知识梳理典例透析随堂演练知识梳理典例透析随堂演练目标导航知识梳理典

31、例透析随堂演练目标导航目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1234566.一个口袋里装有7个白球和1个红球,从口袋中任取5个球.(1)共有多少种不同的取法?(2)其中恰有1个红球,共有多少种不同的取法?(3)其中不含红球,共有多少种不同的取法?