If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
total no for selecting 3 out of 10=10c3=120
no. of ways in which no two married people included= tot- 2 married couple included
2 married couple can be included in 5c1，no. of ways selecting a couple， * 8c1， no. of ways selecting the third person，=5 * 8=40
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方法二：先从5对夫妻里面选3对，再从这3对夫妻里每对各自选一个人出来。C(5,3)*C(2,1)*C(2,1)*C(2,1)=80
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相当于是运用了乘法原理来做的
cool，我跟你一个方法，看到你的评论我放心了很多登录 或 注册 后可以参加讨论
要想选couple，前两个人（即couple）有5种选法，第三个人在剩下的八个人里面选一个，所以是40.
2 married couple can be included in 5c1，no. of ways selecting a couple， * 8c1， no. of ways selecting the third person，=5 * 8=40
但需要再减去有夫妻的组合，有5x8=40种可能
所以120-40=80
但需要再减去有夫妻的组合，有5x8=40种可能
所以120-40=80
有至少一對夫妻： 5C1 x 8C1 = 40
120-40=80
no. of ways in which no two married people included= tot- 2 married couple included
2 married couple can be included in 5c1，no. of ways selecting a couple， * 8c1， no. of ways selecting the third person，=5 * 8=40