In how many ways could a committee of 3 or 4 people be formed from a staff of 15?

Question

In how many ways could a commitee of 3 or 4 people be formed from a staff of 15?

Answer 1

For choice of the first committee member we have 15 to choose from. For the second, 14 to choose from, and so on. So to form a committee of 3 we have 15*14*13 ways of selecting people. However, this selection will include all possible arrangements of the same three people, and there are 6 ways of doing this so, if it’s just the combination of people, and not the order in which they were selected, that matters, we must divide by 6: 15*14*13/6=455.

Similarly, for a committee of 4: 15*14*13*12/24=1365, because there are 24 different ordered arrangements of 4 people, hence the reduction factor.