🎲 Probability Calculator

Permutation & Combination Calculator

Calculate P(n,r) permutations — ordered arrangements — and C(n,r) combinations — unordered selections — with factorials, step-by-step working, and real-world examples.

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Constraints: 0 ≤ r ≤ n ≤ 170 (factorial limit)
Enter n and r above
P(n,r) = n!/(n−r)! · C(n,r) = n!/(r!(n−r)!)

Permutation vs Combination

FeaturePermutationCombination
Order matters?YesNo
Formulan!/(n−r)!n!/(r!(n−r)!)
ExampleLock codesLottery tickets
P(5,2)20—
C(5,2)—10

Frequently Asked Questions

What is the difference between permutation and combination?
Permutation considers ORDER important (ABC ≠ BAC). Combination does NOT consider order (ABC = BAC). Tip: if you're choosing a team, use combinations. If you're choosing a captain + vice-captain, use permutations.
What is n! (factorial)?
n! = n × (n−1) × (n−2) × … × 1. For example, 5! = 5×4×3×2×1 = 120. By definition, 0! = 1.