Enter n (total objects) and r (objects to arrange) to calculate P(n,r) — the number of ordered arrangements using the nPr permutation formula. The result shows how many distinct sequences are possible when order matters and repetition is not allowed. Also try the nCr Calculator.
Permutations P(n,r)
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n! (n factorial)
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(n - r)! Factorial
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Combinations C(n,r) for Reference
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A permutation is a selection of r items from a set of n items where the order in which items are arranged matters. For example, choosing 2 letters from {A, B, C} gives AB and BA as two different permutations, even though they contain the same elements. See also our calculate Combinations C(n,r), Permutations P(n,r) & n! (n Factorial) — Possible Combinations.
The permutation formula is P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number being arranged. The exclamation mark (!) denotes factorial — for example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
Permutations count ordered arrangements — AB and BA are different. Combinations count unordered selections — AB and BA are the same. Use nPr when order matters and nCr when order does not matter.
When r equals n, P(n, n) = n!, meaning all n objects are arranged in every possible order. For example, 3 objects can be arranged in 3! = 6 different ways. You might also find our calculate Password Combination useful.
No. r must be less than or equal to n. If r > n, permutations without replacement are undefined because you cannot choose more items than exist in the set.
No, this calculator computes permutations without repetition — once an object is selected, it cannot be selected again. Permutations with repetition use a different formula: n^r.
Simply enter the total number of objects (n) and the number of objects you want to arrange (r), then the calculator applies P(n, r) = n! / (n - r)! to display your result. Make sure r does not exceed n.
Permutations appear in ranking problems (e.g. gold/silver/bronze from 10 athletes), PIN code creation, seating arrangements, scheduling ordered tasks, and any scenario where sequence matters.