# Your dog has 10 puppies and you are going to keep 3 of them. How many different groups of puppies can you choose?

120

#### Explanation:

This is a combinations question - selecting puppies 1, 2, 3 is the same as choosing puppies 3, 2, 1.

The general formula for a combination is:

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

C_(10,3)=(10!)/((3)!(10-3)!)=(10!)/((3!)(7!))=>

(cancel10^5xxcancel9^3xx8xxcancel(7!))/(cancel3xxcancel2xxcancel(7!))=5xx3xx8=120