Relation Between Permutations and Factorials

Relation Between Permutations and Factorials

## Formula

$$^nP_r=\frac{n!}{(n-r)!}$$

Also:

$$^nP_r=n\cdot{}^{n-1}P_{r-1}$$

and:

$$^nP_r=\frac nr\,{}^{n-1}P_{r-1}$$

## Usage

- Used to simplify permutation expressions and establish relations between different permutation values.