# Permutation

change of ordering in a (mathematical) set

A permutation is a single way of arranging a group of objects. It is useful in mathematics.

A permutation can be changed into another permutation by simply switching two or more of the objects. For example, the way four people can sit in a car is a permutation. If some of them chose different seats, then it would be a different permutation.

## Permutations without repetitions

The factorial has special application in defining the number of permutations in a set which does not include repetitions. The number n!, read "n factorial", is precisely the number of ways we can rearrange n things into a new order. For example, if we have three fruit: an orange, apple and pear, we can eat them in the order mentioned, or we can change them (for example, an apple, a pear then an orange). The exact number of permutations is then $3!=1\cdot 2\cdot 3=6$ . The number gets extremely large as the number of items (n) goes up.

In a similar manner, the number of arrangements of r items from n objects is consider a partial permutation. It is written as $nPr$  (which reads "n permute r"), and is equal to the number $n(n-1)\cdots (n-r+1)$  (also written as $n!/(n-r)!$ ).