factorial

factorial

For any whole number, the product of all the counting numbers up to and including itself. It is indicated with an exclamation point: 4! (read “four factorial”) is 1 × 2 × 3 × 4 = 24. In order for certain formulas involving permutations and combinations to work, 0! is defined to be 1. Factorials are particularly useful in calculating the number of ways an event can occur, for example, the number of possible orders of finish in a race.

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The number of sequences that can exist with a set of items, derived by multiplying the number of items by the next lowest number until 1 is reached. For example, three items have six sequences (3x2x1=6): 123, 132, 231, 213, 312 and 321. See factor and IFP.

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(mathematics)

factorial - The mathematical function that takes a natural number, N, and returns the product of N and all smaller positive integers. This is written N! = N * (N-1) * (N-2) * ... * 1. The factorial of zero is one because it is an empty product. Factorial can be defined recursively as 0! = 1 N! = N * (N-1)! , N > 0 The gamma function is the equivalent for real numbers.