Question

There are 11 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?

Answer 1

We can tell it’s not a permutation because it’s picking two people. Order doesn’t matter.

The number of total possible groups of men is 9 C 2 = 9!/((9-2)!(2!)) = 36

The number of total possible groups of women is 11 C 2 = 11!/((11-2)!(2!)) = 55

55 * 36 = 1980 different groups in the committee