factorial

n! — multiply every whole number from n down to 1.

For a positive integer $n$ , the factorial $n!$ is the product of every positive integer from $n$ down to $1$ : $n!=n\cdot(n-1)\cdots 2\cdot 1$ , with the convention $0!=1$ since there is exactly one way to arrange zero objects: do nothing. Factorials count the number of ways to arrange all $n$ of a set of distinct items in order.

Examples

$5! = 5\cdot4\cdot3\cdot2\cdot1=120$ .