Permutation with Repetition

combinatorics

Definition

Permutation with Repetition

A permutation with repetitions is an ordered rearrangement of $n$ elements consisting of $k$ distinct elements.

All possible permutations of a $n$-tuple can be counted using:

$$\frac{n!}{n_1!n_2!\dots n_k!}$$

where $n_i$ is the number of repetitions of the same element, by the product rule.