Permutation and Combination Calculator
The Permutation and Combination Calculator solves two fundamental problems in combinatorics: how many ways can you arrange or select items from a set? Permutations count ordered arrangements (the order matters), while combinations count unordered selections (order doesn't matter). This calculator handles both cases, with and without repetition, showing every step of the factorial calculation so you can understand the math behind the answer.
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Total items in the set (max 170)
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- •Order matters → Permutation (nPr)
- •Order doesn't matter → Combination (nCr)
- •C(n,r) = C(n, n−r) — symmetric property
- •nCr ≤ nPr always (for same n, r)
functions Formulas
The Formula
Permutations (nPr) count ordered arrangements. Combinations (nCr) count unordered selections. With repetition: nPr = nʳ, nCr = (n+r−1)! / (r!(n−1)!)
nPr = n! / (n−r)! | nCr = n! / (r! × (n−r)!)
lightbulb Variables Explained
tips_and_updates Pro Tips
Use permutation when order matters (e.g., first/second/third place finishes)
Use combination when order doesn't matter (e.g., selecting a team)
nCr is always ≤ nPr for the same n and r
C(n,r) = C(n, n−r) — choosing 3 from 10 = choosing 7 from 10
For repetition allowed: arranging r items from n gives nʳ permutations
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