Problem Solving - 25

Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?

(A) 1/6
(B) 1/4
(C) 2/7
(D) 1/3
(E) 1/2


Answer: E

1st Group: 3 Men, 1 Woman
2nd Group: 1 Man, 2 Women

Total number of ways of selection: 4C2 * 3C2 = 18

No of ways of selecting two men and two women:

1. 2 men and 0 woman from 1st group and 0 men and 2 women from 2nd group = 3C2 = 3
2. 1 man and 1 woman from 1st group and 1 man and 1 woman from 2nd group = 3C1* 2C1 = 6 Thus Total ways from the above = 3 + 6 = 9

Therefore Probability = 9/18 = 1/2