Combination & Permutation Calculator
Compute combinations (order doesn\u2019t matter) and permutations (order matters) for choosing k items from n.
Inputs
Combinations C(n,k)
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Permutations P(n,k)
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Permutations with repetition (n^k)
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Combinations with repetition
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Formula used
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About Combination & Permutation Calculator
Combination vs permutation
Permutation cares about order — ABC, ACB, BAC are different. Combination does not — they\u2019re all the same selection {A,B,C}. P(n,k) = k! × C(n,k).
Real-world examples
Pick 6 lottery numbers from 49: C(49,6) = 13,983,816. License plate (3 letters then 4 digits): 26³ × 10⁴ = 175,760,000 combinations. Order/repetition rules matter a lot.
Pascal\u2019s triangle
Row n of Pascal\u2019s triangle is C(n,0), C(n,1), ..., C(n,n). The classic recursive identity C(n,k) = C(n-1,k-1) + C(n-1,k) lets you compute the triangle row by row.