Permutations & combinations

When order matters, count arrangements by multiplying the number of choices for each position. For $n$ distinct items, the number of possible orders is $n\times (n-1)\times \cdots \times 1$, written $n!$. For example, arranging three items gives $3\times 2\times 1=6$ orders. If you are choosing $r$ items from $n$ and order matters, multiply $n\times (n-1)\times \cdots$ for $r$ factors. If order does not matter, divide by $r!$ to remove duplicate orders of the same group.