A focus group of three people is to be chosen from four pairs of boss-subordinate for a study. What is the number of different focus groups that can be chosen if two people who are boss-subordinate cannot both get in the group ?  Choose the correct choice from the following answers: A) 16 B) 24 C) 26 D) 30 E) 32
Each pair can send only one representative to the focus group. Let's see in how many ways we can choose 3 individuals (as there should be 3 members) out of 4 to send only one representatives to the group : 4C3=4.   But each of these 3 pairs can send two persons (boss or subordinate): 2*2*2=2^3=8.   Total # of ways: 4C3*2^3=32.   Answer: 32.
<result>E</result>
A focus group of three people is to be chosen from four pairs of boss-subordinate for a study. What is the number of different focus groups that can be chosen if two people who are boss-subordinate cannot both get in the group ?