A committee of three people is to be chosen from 6 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?
Select the correct option
A) 16
B) 24
C) 26
D) 30
E) 160
One of the approaches:   Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 6 to send only onerepresentativesto the committee: 6C3=20.   But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.   Total # of ways: 6C3*2^3=160.   Answer: 160.
<result>E</result>
A committee of three people is to be chosen from 6 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?