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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.

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Examples

5-card poker hand
InputC(52, 5)
Output2,598,960 possible hands
Top 3 of 10 racers
InputP(10, 3)
Output720 ordered podium outcomes
Lottery 6 from 49
InputC(49, 6)
Output13,983,816 — your odds of jackpot

Frequently 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.

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Why this tool

vs typical free web-tool sites

1vwTypical free site
PriceFreeFree
Signup requiredNoOften (for premium features)
Ads inside the toolNoYes (banner + video)
Data sent to serverNo (browser-only)Yes (inputs analyzed for ads)
Total tools96Often <20 or scattered across sites
Bookmarkable URL per toolYesMixed
Loads in under 1sYes (static)Often slow (ad tracking)
MultilingualEN / ES / PT / FR / DEUsually EN only
Open sourceYesNo