factorial
(another Prime Pages' Glossary entries)
The Prime Glossary
Glossary: Prime Pages: Top 5000: The factorial of a positive integer is the product of all the positive integers less than or equal to it.  The factorial of n is usually denoted n!  The first few are 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, and 6!=720.  We also define 0! to be 1 (in mathematics, an empty product has the value one). 

n! is the number of permutations of n items (how many ways n distinct items can be arranged in a row).  The number of ways you can pick r or n identical items is the binomial coefficient n!/(r!(n-r)!).

See Also: FactorialPrime, StirlingsFormula, WilsonsTheorem


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