Permutation Calculator (nPr)
Calculate the number of ways to arrange r items from a set of n, where order matters.
Calculate the number of ways to arrange r items from a set of n, where order matters.
How Permutation Calculator (nPr) Works
A permutation counts every distinct ORDERED arrangement of r items chosen from n — since swapping the order creates a new outcome, this number is always larger than the equivalent combination count.
See It In Action
Who Uses Permutation Calculator (nPr) and Why
- Calculating how many different ways the top three finishers in a race could be ordered.
- Figuring out how many distinct passwords or codes are possible when characters can't repeat and their order matters.
- Working out the number of possible seating arrangements for a specific number of people in a row of distinct seats.
Mistakes to Avoid
- Using this calculator when order actually doesn't matter (like picking an unordered group rather than assigning distinct roles) — that scenario calls for the Combination Calculator instead, which will give a smaller number.
- Entering r greater than n — you can't arrange more items than exist in the set.
- Forgetting that repeated items or repeated positions aren't accounted for by the basic nPr formula, which assumes all n items are distinct and none repeat in the arrangement.
Tips for Best Results
- Remember P(n,r) = C(n,r) × r! — every combination of r items can be arranged in r! different orders, which is exactly why the permutation count is always at least as large as the combination count.
- If your scenario has distinct roles (1st place, 2nd place; or specific named seats), that's a strong signal you want permutations, not combinations.
Fixing Common Problems
My permutation result seems too large compared to what I expected. — Double check whether your problem actually cares about order — if different arrangements of the same group shouldn't count separately, you likely want the Combination Calculator instead, which will give a smaller, more appropriate result.
Terms Explained
Permutation: An ordered arrangement of r items chosen from a set of n, where different orderings count as distinct outcomes.
nPr: Standard notation for the number of permutations of r items chosen from a set of n.