Question

In how many ways can a committee of 4 be selected from a group of 12 people?

.

Answer 1

495

Explanation:

We don't care about the order in which people are picked and so this is a combinations question:

`C_(n,k)=((n),(k))=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

`((12),(4))=495`

For anyone who doesn't have Pascal's Triangle saved as a wallpaper, we can work it the long way:

`(12!)/((4!)(8!))=(12xx11xx10xx9)/24=495`