Number of Functions

Number of Functions

## Formula

If:

$$n(A)=m,\qquad n(B)=n$$

then the number of functions from $A$ to $B$ is:

$$n^m$$

## Conditions / Special Cases

Each of the $m$ elements of $A$ has $n$ possible images in $B$.

If:

$$n(B)=1$$

then:

$$n^m=1$$

## Usage

- Used in counting problems involving mappings between finite sets.