# 9 students volunteer for a committee. How many different 7-person committees can be chosen?

36

#### Explanation:

Since the spots in the committee are indistinguishable, we can use the combinations general formula, which is:

C_(n,k)=(n!)/((k!)(n-k)!) with $n = \text{population", k="picks}$

Here we have $n = 9 , k = 7$:

C_(9,7)=(9!)/((7!)(9-7)!)=(9!)/((7!)(2!))=(9xxcancel8^4xxcancel(7!))/(cancel(7!)(cancel2))=9xx4=36