Permutation & Combination Calculator
Compute nPr and nCr, with optional listing of all arrangements or subsets. Bounded for huge counts.
Permutation & Combination Calculator — Permutations and combinations are the two basic ways of counting selections from a set. A permutation is an ordered arrangement — picking 1st, 2nd, 3rd place. A combination is an unordered subset — picking a committee of three.
All calculations run locally in your browser. Nothing is uploaded — close the tab and the data is gone.
What is permutation & combination calculator?
Permutations and combinations are the two basic ways of counting selections from a set. A permutation is an ordered arrangement — picking 1st, 2nd, 3rd place. A combination is an unordered subset — picking a committee of three.
This tool computes nPr and nCr instantly, formats the result with sensible magnitude (3.7 million, 1.2 × 10²⁴, etc.), and — for small enough values — lists every arrangement or subset so you can see the pattern.
How to use it
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Enter n and r
n is the total set size, r is how many you pick.
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Pick permutation or combination
Permutation counts order, combination does not.
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Optionally list the values
Enter items as a comma-separated list, then click List to enumerate.
Examples
Lottery odds
6 numbers from 49, order does not matter.
n = 49, r = 6, combination
Result: 13,983,816 (≈ 14 million)
Race podium
1st, 2nd, 3rd from 8 runners, order matters.
n = 8, r = 3, permutation
Result: 336 (8 × 7 × 6)
Frequently asked questions
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