# 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",[1] 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 ${\displaystyle 3!=1\cdot 2\cdot 3=6}$ . 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 considered a partial permutation. It is written as ${\displaystyle nPr}$  (which reads "n permute r"), and is equal to the number ${\displaystyle n(n-1)\cdots (n-r+1)}$  (also written as ${\displaystyle n!/(n-r)!}$ ).[2][3][4]

## References

1. "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-10.
2. "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-09-10.
3. "Combinations and Permutations". www.mathsisfun.com. Retrieved 2020-09-10.
4. Weisstein, Eric W. "Permutation". mathworld.wolfram.com. Retrieved 2020-09-10.