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.
