Permutations with Repetition of Identical Objects

Permutations with Repetition of Identical Objects

## Formula

If there are $$n$$ total objects with repetitions:

$$n_1,n_2,\ldots,n_k$$

then the number of distinct arrangements is:

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

where:

$$n=n_1+n_2+\cdots+n_k$$

## Usage

- Used for words or arrangements containing repeated identical objects.