[求助]求解一道数学题

cooperqi

A committee of 3 people is to be chosen from 4 married couples, what is the

number of different committee 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

我是这么想的，4couple 一共8个人，先从8个里取一个，然后去掉一个couple，再从6个里取一个，去掉一个couple，再从4个里取一个。但这样算出来数字太大了。正确答案是E，求教是怎么算出来的？

barmecider

2^3 * C34  （C34代表上面是3，下面是4）

你的办法有重叠，除以3！

lixinli

(1C4 * 1C2) * (1C3 * 1C2) * (1C2 *1C2) / 3!

cooperqi

 C38-C14*C16

grace_wang

先去掉一对couple，再从剩下的三对中，每对取一个~这样就避免取到一对儿的啦~

C43*C21*C21*C21=32

audiencer

一共有C38中取法，再减掉取到一对couple的可能性

就是56-4x6=32