A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

answer: 32

我是这样思考的，先从4组中选1组，然后同组中有2种可能被选上；后选出第2组……依次类推

C(4,1)xC(2,1)xC(3,1)xC(2,1)xC(2,1)xC(2,1) =96

大家来看看，我思路哪里不对……

偶觉得这题是问除去一对夫妇 both serve on the committee这种情况之后的the number of different committees

C（8，3）－C（4，1）×C（6，1）＝32

C（8，3）是从4对夫妇也就是8个人中选3个人，这是所有的可能，再减去选出的3人中同时出现一对夫妇的情况，即

C（4，1）×C（6，1）从4对夫妇中取一对，即取了2个人，再从剩下的6个人中取1个人。

只要用总的数量

C（8，3）减去选出一对夫妇的组成数C（4，1）*C（6，1）

56-24=32