Permutation formula
A permutation counts the ways to arrange r items chosen from n when order matters. Because arrangements like AB and BA are counted separately, permutations give larger numbers than combinations.
- n = the total number of items
- r = the number of items chosen and arranged
- n! = n factorial, the product of all whole numbers from 1 to n
When order matters
Use permutations when the sequence is important, such as the finishing order in a race, the digits of a code, or the seating around a table. Choosing the same items in a different order counts as a different permutation. The factorial in the formula accounts for every possible arrangement.
- Choose and arrange 2 items from 5, so n = 5 and r = 2.
- Apply the formula: P(5, 2) = 5! / (5 − 2)! = 5! / 3!.
- That is 120 / 6 = 20.
- There are 20 ordered arrangements.
Related formula
See the Combination Formula for selections where order does not matter.
FAQ
What is the difference between a permutation and a combination?
A permutation counts ordered arrangements; a combination counts selections where order does not matter. Permutations give larger counts.
What does n! mean?
n factorial is the product of all whole numbers from 1 up to n. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.