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作者: michellenana 时间: 2009-6-17 16:18
标题: 完了···请教！！

脑子秀逗了··排列组合做不来了

请教一题：

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?

作者: usocean 时间: 2009-6-17 16:55

以下是引用michellenana在2009-6-17 16:18:00的发言：

脑子秀逗了··排列组合做不来了

请教一题：

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?

5对夫妇，选3个人出来，任意2个人不能是夫妻，有多少种选法。

C 10 3 - (C 8 1)*5 = 80

作者: michellenana 时间: 2009-6-17 17:06
谢楼上滴```

作者: 歌霏 时间: 2009-6-17 17:56

以下是引用usocean在2009-6-17 16:55:00的发言：

5对夫妇，选3个人出来，任意2个人不能是夫妻，有多少种选法。

C 10 3 - (C 8 1)*5 = 80

请问(C 8 1)*5 表示挑选出来的人中有2个是夫妻是么？

可否详细讲一下为何这么写？

我的思路是先选出3对couple，然后从每对couple中挑出一个人来组成committee，所以是 C(5,3)*3C(2,1)=60

作者: bonjourguan 时间: 2009-6-17 18:08
(C 8 1)*5 表明5对中随便挑一对,然后剩下八个人中再挑一个, 这个是肯定"include two people who are married to each other"; 如果按照你的思维,算法应该为(C5 3)*(C2 1)*(C2 1)*(C2 1)=80,即随5对随便挑3对,三对中每个都2选一

作者: 歌霏 时间: 2009-6-17 21:32

对对对，我也同意楼上的，2楼的gg，你的方法是说，挑选中的3个人中，肯定有两个人是夫妻，而不是原题的“the committee does not include two people who are married to each other”。

另外，我之前考虑欠妥，应该是楼上的 (C5 3)*(C2 1)*(C2 1)*(C2 1)=80

作者: kuannn 时间: 2018-3-21 10:59
感謝bon的詳盡解釋！！！

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