# Permutations

Permutations are multiplicative events where the number of possibilities is decreasing and whether it is important the order of a permutation, it is an arrangement of a set of objects in a defined order.

The number of possible permutations to take objects from the set of elements will be, following the same argumentation:

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Permutations can be:

• Without repetition of n items taken all at once.

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• Permutations without repetition of n elements taken in groups of r ítems.

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• With repetition of n elements taken in groups of r ítems.

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• Permutations of n elements which h is from a type, j is from other, etc. In this case, all the elements enter, the order does matter and the elements are repeated.

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• Circular Permutations. These are used when elements have to be ordered “in circle” so that the first element that “take place” in the sample determines the beginning and end of the sample.

(For example, commensals at a table)

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It must be clear that the factorial function (symbol: ! ) means that all smaller numbers are multiplied:

Example:

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