The number n! is the product 1 x 2 x 3 x 4 x ... x n, that is, the product of all the natural numbers from 1 up to n, including n itself where 1 is a natural number. It is called either "n factorial" or "factorial n." Thus 5! is the number 1 x 2 x 3 x 4 x 5, or 120.

Older books sometimes used the symbol In for n factorial, but the numeral followed by an exclamation point is currently the standard symbol.

Factorials show up in many formulas of statistics, probability, combinatorics, calculus, algebra, and elsewhere. For example, the formula for the number of permutations of n things, taken n at a time, is simply n!. If a singer chooses eight songs for his or her concert, these songs can be presented in 8!, or 40,320 different orders. Similarly the number of combinations of n things r at a time is n! divided by the product r!(n...