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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, 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! 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 e.g. an apple, then a pear and finally an orange. The exact number of permutations is then [math]3! = 1 \cdot 2 \cdot 3 = 6[/math]. The number gets extremely large as the number of items (n) goes up.