# How do you calculate combinations of things?

Oct 31, 2014

Combinations of items are basically subsets of the items, so the number of combinations is the number of subsets of items.

Let $C \left(n , r\right)$ denote the number of combinations of $n$ item chosen $r$ items at a time. Then, it can be found by

C(n,r)={P(n,r)}/{r!}={n cdot (n-1) cdot (n-2) cdot cdots cdot (n-r+1)}/{r!}={n!}/{(n-r)! r!}

Example

Find the number of ways to choose 3 cookies out of 6 distinct cookies.

C(6,3)={P(6,3)}/{3!}={6cdot5cdot4}/{3cdot2cdot1}=20

Hence, there are 20 ways to choose 3 cookies from 6 cookies.

I hope that this was helpful.