Restricted Selection

Restricted Selection

## Definition / Concept

When a selection must contain or exclude certain objects, count the restricted cases directly or use complementary counting.

## Formula

If a selection of $$r$$ objects from $$n$$ objects must contain a particular object:

$${}^{n-1}C_{r-1}$$

If it must exclude that particular object:

$${}^{n-1}C_r$$

## Usage

- Used when specific objects are required or prohibited in a selection.