Mathegoras

Generalized Permutations and Combinations

Published On :2021-02-09 23:19:00

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We want to solve counting problems where element maybe used more than once .

* Permutation with repetition

The number of r-permutations from a set of n-elements with repetition allowed is

[{n^r}]

* Combination with repetition

The number of r-combinations from a set of n-elements with repetition allowed is

[left( {begin{array}{*{20}{c}} {n - 1 + r}\ {n - 1} end{array}} right) = left( {begin{array}{*{20}{c}} {n - 1 + r}\ r end{array}} right)]