Question

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

Answer 1

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="population", k="picks"`

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

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