Factorial

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The factorial of a whole number n, written as n!,[1] is found by multiplying n by all the whole numbers less than it. For example, the factorial of 4 is 24, because 4 × 3 × 2 × 1 = 24. Hence one can write 4! = 24. For some technical reasons, 0! is equal to 1.[2]

Factorial can be used to find out how many possible ways there are to arrange n objects.[2]

For example, if there are 3 letters (A, B, and C), they can be arranged as ABC, ACB, BAC, BCA, CAB, and CBA. That would be 6 choices because A can be put in 3 different places, B has 2 choices left after A is placed, and C has only one choice left after A and B have been placed. In other words, 3×2×1 = 6 choices.

The factorial function is a good example of recursion (doing things over and over), as 3! can be written as 3×(2!), which can be written as 3×2×(1!) and finally as 3×2×1×(0!). N! can therefore also be defined as N×(N-1)!,[3] with 0! = 1.[2]

The factorial function grows very fast. There are 10! = 3,628,800 ways to arrange 10 items.[3]

Notes[change | change source]

n! is not defined for negative numbers. However, the related gamma function is defined over the real and complex numbers (but the integers it is defined over are positive).[2]

Related pages[change | change source]

References[change | change source]

  1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-09.
  2. 2.0 2.1 2.2 2.3 Weisstein, Eric W. "Factorial". mathworld.wolfram.com. Retrieved 2020-09-09.
  3. 3.0 3.1 "Factorial Function !". www.mathsisfun.com. Retrieved 2020-09-09.

Other websites[change | change source]