Permutations and Combinations

Formulas for Arrangements

If you want to find the number of possible arrangements of $n$ objects, use $n!$ where

In other words, multiply together all the numbers from $n$ down to 1.
If you are arranging $n$ objects in a circle, then there are $(n-1)!$ possible arrangements.

Arranging by Type

If you want to arrange $n$ objects where $j$ of one type are alike, $k$ of another type are alike, so are $m$ of another type and so on, the number of arrangements is given by

Permutations

If you choose $r$ objects from a pool of $n$, the number of permutations is given by

permutations are when you care about the order of the objects you select

Combinations

If you choose $r$ objects from a pool of $n$, the number of combinations is given by

combinations are where you only care which objects are selected, not their order

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