Permutation and Combination: Factorial

Concept Explanation

Factorial n! is the product of all positive integers from 1 to n. It forms the basis of permutations and combinations.

Key Formulas

• n! = n × (n − 1) × … × 2 × 1
• 0! = 1 (by definition)
• n! / (n − r)! = n × (n − 1) × … × (n − r + 1)

Example

5! = 5 × 4 × 3 × 2 × 1 = 120.

Common Trap

Do not treat 0! as 0. Remember 0! = 1.