Question

How do you calculate combinations of things?

Answer 1

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!}`

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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.

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I hope that this was helpful.