# Difference between revisions of "Factorial"

The factorial is an important function in combinatorics and analysis, used to determine the number of ways to arrange objects.

## Contents

### Definition

The factorial is defined for positive integers as $n!=n \cdot (n-1) \cdots 2 \cdot 1$ Alternatively, a recursive definition for the factorial is: $n!=n \cdot (n-1)!$.

By convention, $0!$ is given the value $1$.

The gamma function is a generalization of the factorial to values other than nonnegative integers.

### Uses

The factorial is used in the definitions of combinations and permutations, as $n!$ is the number of ways to order $n$ distinct objects.