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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, 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 [math]3! = 1 \cdot 2 \cdot 3 = 6[/math]. 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 [math]nPr[/math] (which reads "n permute r"), and is equal to the number [math]n (n-1) \cdots (n - r + 1)[/math] (also written as [math]n! / (n-r)![/math]).
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