## DEFINITION of 'Permutation'

In mathematics, one of several ways of arranging or picking a set of items. The number of permutations possible for arranging a given a set of n numbers is equal to n factorial (n!). So, a set of three numbers can be arranged as: 3x2x1 = 6 permutations. Another type of permutation involves choosing a set of i items out of n choices. In this case, the number of permutations for choosing i items given n choices is given by n!/[(n-i)!]. Permutations are applicable to sets where the order matters; order does not matter in combinations.

## BREAKING DOWN 'Permutation'

The study of permutations applies to finance in a broad sense because a good understanding of probability is sometimes necessary to make rational financial choices. The Allais paradox problem shows that on their own, people do not instinctually choose the higher expected financial reward. Given the choice between a sure amount of money and a small gamble with a higher expected value, most people choose the guaranteed amount due to behavioral biases. Financial professionals must be able to rationally evaluate such situations and make the correct choices on behalf of shareholders or clients.