Grade 12 · Mathematics
Permutations
Why it matters
Ordered arrangements.
Last reviewed 2026-09-03 · accuracy standard
What is a permutation?
Short answer
A permutation is an arrangement of objects in which order matters. The number of ways to arrange r objects chosen from n distinct objects is nPr = n! / (n − r)!. For example, arranging 3 of 5 books on a shelf gives 5P3 = 60 orders. Permutations differ from combinations, where order does not matter.
Concept preview
What you will be able to do
- 01Distinguish ordered selections (permutations) from unordered ones (combinations)
- 02Apply the formulas for and
- 03Count committees, teams, and hands, including 'at least' and case problems
The single question that decides every problem in this section is: does order matter? If arranging the same items differently counts as a new outcome, it is a permutation (ordered). If only which items are chosen matters, not their order, it is a combination (unordered). Choosing a president then a vice-president is a permutation (the roles differ); choosing a two-person committee is a combination (the two are interchangeable).
School Plan
Permutations
This lesson's full explanation, worked examples, quiz and practice are locked. Full access is on the School Plan.
Log in or start free and you will return right here.
Related topics
Frequently asked questions
- What is the difference between a permutation and a combination?
- A permutation counts arrangements where order matters; a combination counts selections where order does not.
- What does n! mean?
- n factorial is the product of all positive integers up to n: for example 5! = 5·4·3·2·1 = 120.