A permutation refers to a specific ordering of the elements of a set. For example 5♥ 7♦ 2♠ is a permutation of three poker cards. Unlike a combination the ordering is important.

The above is a table of the number of permutations of cards from a standard poker deck. For contrast the number of combinations is also shown.

Calculation

Though sometimes relevant, one does not normally wish to permute every member of a set. In poker for example only short permutations, or 3 or 4 cards, are usually interesting.

The calculation is an application of the factorial function. In short form the permutation can be expressed as (nPk) which is the same as n! / (n-k)!. Where factorial is simply that number, and every one less than it to 1 multiplied together.