Question

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

Answer 1

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="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`