# Difference between revisions of "Factorial"

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The factorial is used in the definitions of [[combinations]] and [[permutations]], as <math>n!</math> is the number of ways to order <math>n</math> distinct objects. | The factorial is used in the definitions of [[combinations]] and [[permutations]], as <math>n!</math> is the number of ways to order <math>n</math> distinct objects. | ||

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+ | === Examples === | ||

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+ | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=508851#p508851 AIME 2003I/1] | ||

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+ | === See also === |

## Revision as of 10:24, 19 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 Alternatively, a recursive definition for the factorial is: .

### Additional Information

By convention, is given the value .

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 is the number of ways to order distinct objects.