Difference between revisions of "Factorial"
From ScienceZero
(New page: The factorial <math>n!</math> gives the number of ways in which <math>n</math> objects can be permuted. For example, <math>3!=6</math>, since the six possible permutations of {1,2,3} are {...) |
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− | The factorial | + | The factorial '''n'''! gives the number of ways in which '''n''' objects can be permuted. For example, 3! = 6, since the six possible permutations of {1,2,3} are {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1}. !0 is defined as 1 just as an empty set {} has one possible permutation {}. |
Revision as of 17:30, 30 January 2007
The factorial n! gives the number of ways in which n objects can be permuted. For example, 3! = 6, since the six possible permutations of {1,2,3} are {1,2,3}, {1,3,2}, {2,1,3}, {2,3,1}, {3,1,2}, {3,2,1}. !0 is defined as 1 just as an empty set {} has one possible permutation {}.
- 0! = 1
- 1! = 1
- 2! = 1*2 = 2
- 3! = 1*2*3 = 6
- 4! = 1*2*3*4 = 24
- 5! = 1*2*3*4*5 = 120
- 20! = 1*2...19*20 = 2 432 902 008 176 640 000