Permutation Calculator (nPr)
Permutation Calculator (nPr)
The permutation calculator finds how many ways you can arrange r items from a group of n items when order matters.
Conversion Formula
P(n, r) = n! / (n - r)!. This multiplies n × (n-1) × (n-2) × ... for r terms.
Step-by-Step Examples
n = 10, r = 3 = 720
There are 720 ways to award gold, silver, and bronze to 3 of 10 athletes.
n = 5, r = 5 = 120
5! = 120 ways to arrange all 5 items.
Frequently Asked Questions
What is a permutation?
A permutation is an arrangement of items where order matters. {A, B, C} and {C, B, A} are different permutations.
When do I use permutations vs combinations?
Use permutations when order matters (rankings, sequences, passwords). Use combinations when order doesn't matter (teams, groups, selections).
What is nPr?
nPr (read "n permute r") is the number of ways to arrange r items from n items in a specific order.
What is P(n, n)?
P(n, n) = n!, which is the number of ways to arrange all n items. For example, P(5,5) = 120.
How are permutations used in real life?
PIN codes, license plates, race finishing orders, seating arrangements, and password possibilities all involve permutations.