A committee of three people is to be chosen from 3 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? Choices:  A) 12  B) 24  C) 26  D) 30  E) 32
One of the approaches:   Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 2 couples (as there should be 2 members) out of 3 to send only onerepresentativesto the committee: 3C2=3.   But each of these 3 couples can send two persons (husband or wife): 2*2=2^2=4.   Total # of ways: 3C2*2^2=12.   12nswer: 12.
<result>A</result>
A committee of three people is to be chosen from 3 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?