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  

$$\left(\begin{array}{c}n-1+r\\ n-1\end{array}\right)=\left(\begin{array}{c}n-1+r\\ r\end{array}\right)$$