Grade 12 · Mathematics
Permutations
Why it matters
Ordered arrangements.
Advanced20m readingPrerequisite: Counting principles
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.
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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.