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Permutations

A permutation is an arrangement in which all n elements are used - geometry homework help (i.e. distributed over n places). A distinction is made between permutations without and with repetition (of the elements).

The problem of arranging n objects (persons, objects, numbers or the like) in a row, i.e. distributing them over n places, leads to the concept of permutation - math problem solver . Every possible arrangement of n elements in which all elements are used is called a permutation Pn of these elements.

A distinction is made between permutations without repetition (of the elements) and permutations with repetition (of the elements).

Of n different elements there are

Pn=n⋅(n-1)⋅...⋅3⋅2⋅1=n ! (n∈N)

Possibilities of such an arrangement (permutations without repetition).

Note: For the product of consecutive natural numbers from 1 to n - do my homework , one uses the abbreviation n! (pronounced: n-faculty).

Example 1:

From the three elements of the set {a; b; c} the following six permutations can be formed:

abc acb bac bca cab cba

Note: When writing down all possible permutations of n elements, it is convenient to keep to a certain order. Usually, one chooses the so-called lexicographic order, in which the order of the elements is determined by the alphabet (or, in the case of numbers, by order according to their size).

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