Carcass wrote:
At a dance there are three married couples: Ann and Andy, Betty and Boris, and Danielle and Dan. The wives select a husband at random with whom to share a dance. What is the probability that each of the three men dances with a woman other than his spouse.
A. 1/9
B. 2/9
C. 1/3
D. 1/2
E. 2/3
Since there are very few outcomes in the scenario, a quick (and reliable) approach is to simply list all of the outcomes.
Let a, b, and c = the three men.
Let A, B, and C = the three women.
The outcomes are:
1) a-A, b-B, and c-C (each spouse matched with their partner)
2) a-A, b-C, and c-B
3) a-B, b-A, and c-C
4) a-B, b-C, and c-A
5) a-C, b-A, and c-B
6) a-C, b-B, and c-ASo, there are 6 possible outcomes, and 2 of those outcomes are such that each of the three men dances with a woman other than his spouse.
So the probability = 2/6 = 1/3
Answer: C