Calculate permutations P(n,r) = n!/(n-r)!, the number of ways to arrange r items from n where order matters. Supports with and without repetition.
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Calculate permutations instantly with our easy-to-use calculator. Find the number of ways to arrange r items from n items where order matters. Perfect for probability, combinatorics, and statistics problems.
A permutation is an arrangement of items where the order matters. P(n,r) represents the number of ways to arrange r items from a set of n items. For example, arranging 3 books from a shelf of 10 books - the order ABC is different from BAC. Without repetition: P(n,r) = n!/(n-r)!. With repetition: P(n,r) = n^r.
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In permutations, order matters (ABC ≠ BAC). In combinations, order doesn't matter (ABC = BAC). Use permutations when arranging items in a specific order, like assigning positions or creating passwords.
Use permutation with repetition when items can be reused. For example, creating a 4-digit PIN where digits can repeat (like 1123). Without repetition, each item can only be used once.
Without repetition: P(n,r) = n!/(n-r)! where n is total items and r is items to arrange. With repetition: P(n,r) = n^r. For example, P(5,3) without repetition = 5!/(5-3)! = 120/2 = 60.
nPr (also written ₙPᵣ or P(n,r)) is the number of permutations — the count of ways to arrange r items from n when order matters. It equals n!/(n-r)!. For example, 8P3 = 336.