+487 There are 3 math clubs in the school district, with 5, 7, and 8 students respectively. Each club has two co-presidents. If I randomly select a club, and then randomly select three members of that club to give a copy of Introduction to Counting and Probability, what is the probability that two of the people who receive books are co-presidents?
For the first math club, there is a 3/5 probability that two of the people that receive books are co-presidents.
For the second math club, there is a 1/7 probability that two of the people that receive books are co-presidents.
For the third math club, there is a 3/28 probability that two of the people that receive books are co-presidents.
The final answer is then (3/5 + 1/7 + 3/28)/3 = 17/60.
