Generalized Permutations and Combinations



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  


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

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