Twelve individuals want to form a committee of four How many

Twelve individuals want to form a committee of four. How many committees are possible? The 12 individuals consist of 5 biologists, 4 chemists, and 3 physicists. How many committees consisting of 2 biologists, 1 chemist, and 1 physicist are possible? In the setting of part (b), if all committees are equally likely, what is the probability the committee formed will consist of 2 biologists, 1 chemist, and 1 physicist?

Solution

a) (5C2)*(4C1)*(3C1) = 120 b) probability = 120 / (12C4) = 0.242