How do you calculate combinations of things?

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Answer 1 · 2014-10-31T17:06:59

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

Let $C(n,r)$ 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.