数学

thumbbunny

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?

(A)  16
(B)  24
(C)  26
(D)  30
(E)  32
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【答案】E
【思路】<作法1>committe中不能有couple的組合即 "全部的組合-committe中有couple的組合"
C(8,3)-4*6
=56-24
=32

不明白4*6是什么意思

sally77589

4*6是指的是有couple在committe中的情况
因为是3个人，所以只有可能是1对couple在committee，有4对couple。C41选中一对以后，其他6个人中选出一人，就是C61，于是用总的C83-C41*C61