š² Combinations & Permutations Calculator
Calculate C(n,r) combinations and P(n,r) permutations for probability, statistics, and counting problems.
Choose n and r
Combinations C(n,r)
Order doesn't matter
Order doesn't matter
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Permutations P(n,r)
Order matters
Order matters
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n! (n factorial)
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r! (r factorial)
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(nār)! factorial
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Perm / Comb Ratio
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Combinations vs Permutations
Combination: Selecting items where order does NOT matter. "Choose 3 flavors from 10" ā {vanilla, chocolate, mint} is the same as {mint, vanilla, chocolate}.
Permutation: Arranging items where order DOES matter. "Top 3 finishers in a race of 10" ā first, second, third placements are distinct.
C(n,r) = n! / (r! Ć (nār)!) "n choose r"
P(n,r) = n! / (nār)!
Relationship: P(n,r) = C(n,r) Ć r!
P(n,r) = n! / (nār)!
Relationship: P(n,r) = C(n,r) Ć r!
Quick Examples
- Lottery (pick 6 of 49): C(49,6) = 13,983,816 combinations
- Password (4 letters AāZ): P(26,4) = 358,800 (no repeats)
- Committee of 3 from 8: C(8,3) = 56 committees