Distribution of Distinct Objects with Non-Empty Groups

Distribution of Distinct Objects with Non-Empty Groups

## Formula

If $$n$$ distinct objects are distributed among $$r$$ distinct persons such that every person receives at least one object, the number of distributions is:

$$r!S(n,r)$$

where $S(n,r)$ is the Stirling number of the second kind.

## Usage

- Used when distinct objects must be distributed among distinct recipients with no recipient left empty.