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nCr Combinations & Permutations
Combinations (nCr) count ways to choose r items from n where order does not matter — used for lottery odds, poker hands, sample selection. Permutations (nPr) count when order matters — used for race finishes, password schemes, arrangements.
Examples
C(52, 5)2,598,960 possible handsP(10, 3)720 ordered podium outcomesC(49, 6)13,983,816 — your odds of jackpotFrequently asked questions
When to use combinations vs permutations?
Order matters → permutations. Order doesn't matter → combinations. "Best 3 of 10" = combinations (3-person committee). "1st/2nd/3rd of 10" = permutations.
What is n factorial (n!)?
n × (n-1) × (n-2) × … × 1. 5! = 120. Defines how many ways to arrange n distinct items.
Why so big so fast?
Factorials grow super-exponentially. 10! is ~3.6M. 20! is 2.4 quintillion. They quickly exceed JavaScript number precision; we use BigInt for large values.
About this tool
Combinations & Permutations runs entirely in your browser using standard Web APIs. No data is sent to any server. The source for this tool is in our public GitHub repository.
Related tools
- 📊 Statistics Calculator — Mean, median, mode, standard deviation, variance, range from a number list.
- ➗ GCD / LCM Calculator — Find greatest common divisor and least common multiple of any numbers.
- 📊 Quadratic Equation Solver — Solve ax² + bx + c = 0 — real and complex roots.
Why this tool
vs typical free web-tool sites
| 1vw | Typical free site | |
|---|---|---|
| Price | Free | Free |
| Signup required | No | Often (for premium features) |
| Ads inside the tool | No | Yes (banner + video) |
| Data sent to server | No (browser-only) | Yes (inputs analyzed for ads) |
| Total tools | 96 | Often <20 or scattered across sites |
| Bookmarkable URL per tool | Yes | Mixed |
| Loads in under 1s | Yes (static) | Often slow (ad tracking) |
| Multilingual | EN / ES / PT / FR / DE | Usually EN only |
| Open source | Yes | No |