Difference between revisions of "Factorial"

(added 2003I/1)
m (See also: added link)
Line 20: Line 20:
  
 
=== See also ===
 
=== See also ===
 +
*[[Combinatorics]]

Revision as of 14:10, 23 June 2006

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

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: $n!=n \cdot (n-1)!$.

Additional Information

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

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

Examples

See also

Invalid username
Login to AoPS