Number Formation Without Repetition

Number Formation Without Repetition

## Definition / Concept

When numbers are formed from given digits without repetition, the first position may have additional restrictions because zero cannot occupy the first position of a multi-digit number.

## Formula

If $$n$$ non-zero digits are available and $$r$$ positions are to be filled:

$${}^nP_r$$

If zero is also available and a $$k$$-digit number is formed from $$n$$ non-zero digits plus zero:

$$n\cdot{}^nP_{k-1}$$

when repetition is not allowed.

## Usage

- Used in digit-arrangement problems involving restrictions on the first digit.