Permutations with Objects Not Together

Permutations with Objects Not Together

## Formula

If $$r$$ specified objects must not be together, use:

$$\text{Required arrangements}=\text{Total arrangements}-\text{Arrangements where they are together}$$

For $$r$$ specified objects among $$n$$ distinct objects:

$$n!-(n-r+1)!r!$$

## Usage

- Used when certain objects are prohibited from appearing as one consecutive block.