What is a permutation?
An arrangement where order matters. Picking a gold, silver and bronze medallist from 8 runners is a permutation, because first and second are different outcomes.
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Permutation Calculator
How many ordered arrangements of r items can be drawn from n, where order matters.
nPr = n! / (n − r)!
Frequently asked questions
How is it different from a combination?
Order. Permutations count 'AB' and 'BA' as two different results; combinations treat them as the same selection. That is why nPr is always at least as big as nCr.
What does the formula n! / (n-r)! actually do?
It counts the choices at each step: n options for the first pick, n-1 for the second, and so on for r picks. The factorial fraction is a tidy way to write that running product.
What is a factorial?
n! means multiply every whole number from 1 up to n. So 5! = 5x4x3x2x1 = 120. It counts the ways to arrange n distinct items in a row.
Where do permutations show up?
PIN codes and passwords, race finishing orders, seating arrangements, and any lock or code where the sequence is what counts.