Combinatorics

Combinatorics is the mathematical field of counting. An application are discrete distributions in simple probability theory.

Factorial

The factorial of a non-negative integer \(n\) is the integer

\[\begin{equation*} n!:=1\cdot 2\cdot\cdots\cdot(n-1)\cdot n, \end{equation*}\]

where \(0!:=1\).

Obviously, \(n!=(n-1)!\,n\).