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What is a factorial?

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Quick answer

A factorial, written with an exclamation mark (like 5! ), means multiplying a whole number by every whole number below it down to 1. So 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials count how many ways things can be arranged.

A factorial, written with an exclamation mark (like 5!), means multiplying a whole number by every whole number below it down to 1. So 5! = 5 × 4 × 3 × 2 × 1 = 120. Factorials count how many ways things can be arranged.

Key things to understand

  1. n! means n × (n−1) × … × 1.
  2. For example, 4! = 4 × 3 × 2 × 1 = 24.
  3. By definition, 0! = 1.
  4. They count arrangements, key to permutations and probability.

People also ask

What is a factorial?
The product of a whole number and all smaller positive whole numbers, written like 5! = 120.
What is 0 factorial?
By definition, 0! equals 1 — there's exactly one way to arrange nothing.
What are factorials used for?
Counting arrangements and selections, which is central to permutations, combinations, and probability.