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.
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.
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.
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.