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标题: 求助这题怎么做，谢谢． [打印本页]

作者: whx1862 时间: 2010-4-20 23:19
标题: 求助这题怎么做，谢谢．
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?

A.20
B.40
C.50
D.80
E.120
Answer:
答案是Ｄ，我做的是Ａ

作者: tristanwhistle 时间: 2010-4-20 23:30
C53(5在下面，三在上面)*2*2*2

作者: tanjing 时间: 2010-4-20 23:33
5*2*C(4,2)+2*C(5,3)

作者: Avène 时间: 2010-4-20 23:56

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?

A.20
B.40
C.50
D.80
E.120
Answer:
答案是Ｄ，我做的是Ａ

-- by 会员 whx1862 (2010/4/20 23:19:52)

这三人全是男人：C53 （5在下，3在上）
全是女人：C53
在男或女中选1人：C51乘以C42 （因为不能使他老婆或她老公）
在男或女中选2人：C52乘以C31
=80

作者: selfay 时间: 2010-4-21 00:20
之前是按照4楼那样做的，刚突然傻掉了，不是这样做，发现没算对，最后总算搞明白了，因为今晚是这样算的
C(5,3)P(2,2)P(2,2)P(2,2)=80

5对夫妇选3对，每对选一个人，等于3对都各自做全排列

作者: whx1862 时间: 2010-4-21 09:17
Thank you.

作者: kaoruya 时间: 2010-4-21 12:31
2楼的解法很清晰啊。。
C(10,3)-C(5,1)*C(8,1)=80
C(10,3)代表10人选3个；C(5,1)*C(8,1)代表5对选1对（2个人了）再从剩下8个人里选1个--就是要排除的选法。

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