Combination & Permutation Calculator
Calculate C(n,r) combinations, P(n,r) permutations and n! factorial with exact results.
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Combination vs. Permutation
Both count ways of choosing r items from n. In a permutation order matters: P(n,r) = n! ÷ (n−r)!. In a combination order does not matter: C(n,r) = n! ÷ (r! × (n−r)!). Choosing 3 officers (president, secretary, treasurer) from 10 people is a permutation (720 ways); choosing a 3-person committee is a combination (120 ways).
The tool computes exact values using big-integer arithmetic, so results do not lose precision even for large n.
Frequently Asked Questions
When do I use combination vs. permutation?
Ask whether order matters. Lottery numbers, committees and card hands are combinations; passwords, rankings and podium finishes are permutations.
What is 0! and why?
By definition 0! = 1. This convention keeps the formulas consistent — e.g. C(n,n) = n! ÷ (n! × 0!) = 1, which is correct: there is exactly one way to choose everything.
How large can n be?
The tool uses exact big-integer arithmetic up to n = 5000, far beyond what floating-point calculators handle without rounding errors.
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Combination & Permutation Calculator