Permutations with Restrictions

Permutations with Restrictions

## Definition / Concept

When certain arrangements are prohibited or specific objects are required to occupy particular positions, the problem is solved by applying the restriction first and then arranging the remaining objects.

## Formula

If one specific object must occupy a fixed position among $$n$$ distinct objects:

$$(n-1)!$$

arrangements are possible.

If $$r$$ specific objects must occupy specified positions:

$$(n-r)!$$

arrangements are possible.

## Usage

- Used for restricted arrangement problems involving fixed positions.