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Permutation & Combination
Calculate permutations and combinations
How It Works
Permutations and combinations are ways to calculate the number of possible arrangements of items. Permutations consider order important, while combinations do not.
Permutations and combinations are part of combinatorial mathematics. A permutation is an arrangement of items in a specific order, while a combination is a selection of items without regard to order.
Permutations count the number of ways to select and arrange r items from a set of n distinct items. For example, choosing 3 winners for gold, silver, and bronze medals from 10 athletes involves permutations because the order (which medal) matters.
Combinations count the number of ways to select r items from n items where order does not matter. For example, choosing 3 finalists from 10 contestants where all finalists are equal involves combinations.
When repetition is allowed, the formulas change: permutations with repetition gives nʳ possibilities, while combinations with repetition gives C(n+r−1, r) possibilities.
Results
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Quick Tips
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