factorial:

The factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$.

The factorial of $n$ also equals the product of $n$ with the next smaller factorial:

$$n!=n\times (n-1)\times (n-2)\times \cdots \times 3\times 2\times 1$$ $$n!=\{\begin{array}{ll}1,& \text{if }n=0\\ n\times (n-1)!,& \text{if }n\ge 1\end{array}$$

Example:

$$5!=5\times 4!=5\times 4\times 3\times 2\times 1=120$$

The value of $0!$ is defined as $1$ (empty product convention).

https://en.wikipedia.org/wiki/Factorial

useful for calculating total number of distinct combinations (3 letter code) 3!.