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Combination Calculator

C(n, r) = n! / (r!(n − r)!) for unordered selections.

Best for: Use it for lottery odds, committees, hands of cards, or any selection where order is irrelevant.

Complete guide

Input

How it's calculated & sources
The Combination Calculator uses the standard, deterministic formula, so the same inputs always produce the same result. It runs entirely in your browser, so your inputs are never uploaded. Last reviewed June 2026.

Free & no sign-up · runs entirely in your browser. Results are estimates for general information, not professional advice — verify important decisions with a qualified expert. Last reviewed June 2026.

How it works

C(n, r) = n! / (r!(n − r)!) — unordered selections.

Example

C(5, 2) = 10

Frequently asked questions

Where is this used?+

Lottery odds, poker hands, committee selection — anywhere order doesn't matter.

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Complete guide

Quick answers

Short, sourced answers to the questions people (and AI assistants) ask most.

What is Combination?
A combination calculator counts how many unordered groups of r items can be chosen from n items.
Why does Combination matter?
The number of distinct groups, ignoring order. nCr is always less than or equal to nPr.
How is Combination calculated?
It divides n factorial by r factorial times (n - r) factorial, because order does not matter. Formula: nCr = n! / (r! (n - r)!).
What are common combination mistakes?
Using combinations when order actually matters (use permutations).
When should you use the Combination Calculator?
Use it for lottery odds, committees, hands of cards, or any selection where order is irrelevant.

What is the Combination Calculator?

A combination calculator counts how many unordered groups of r items can be chosen from n items.

How the Combination Calculator works

It divides n factorial by r factorial times (n - r) factorial, because order does not matter.

nCr = n! / (r! (n - r)!)

Combinations C(n, r) — number of ways to choose r from n

5101051
61520156
721353521
828567056
93684126126
1045120210252

Common mistakes to avoid

  • Using combinations when order actually matters (use permutations).
  • Requiring r greater than n.
  • Forgetting nC0 and nCn both equal 1.

Keywords: combination, ncr.

Reviewed by the Free Tools Galaxy editorial team · Updated June 2026 · Calculated privately in your browser.

Frequently asked questions

Is the Combination Calculator free to use?+

Yes. Every tool on Free Tools Galaxy is 100% free, runs in your browser and requires no signup.

How accurate is the Combination Calculator?+

Combination Calculator uses the standard combination formula in double-precision arithmetic, so the same inputs always produce the same result and you can verify any figure by hand. It is an educational estimate — real-world outcomes depend on your actual rates, rules and assumptions.

Do you store my inputs?+

No. The Combination Calculator runs entirely in your browser. Nothing is uploaded or saved to a server.

Can I use the Combination Calculator on mobile?+

Yes — the interface is fully responsive and works on phones, tablets and desktops.

What are common mistakes to avoid?+

The most frequent mistake is mixing units. Double-check your inputs use a single, consistent unit before clicking Calculate.

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Title: I built/used this free combination calculator — instant, no signup

Body: C(n, r) = n! / (r!(n − r)!) for unordered selections. Try it: https://freetoolsgalaxy.com/tools/combination-calculator
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Combination Calculator on Free Tools Galaxy — C(n, r) = n! / (r!(n − r)!) for unordered selections. https://freetoolsgalaxy.com/tools/combination-calculator
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# Combination Calculator — the free tool I keep coming back to

C(n, r) = n! / (r!(n − r)!) for unordered selections.

Try it: https://freetoolsgalaxy.com/tools/combination-calculator
Quora answer
The fastest way is to use a free in-browser combination calculator: https://freetoolsgalaxy.com/tools/combination-calculator. C(n, r) = n! / (r!(n − r)!) for unordered selections.

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I built a free pregnancy due date calculator that works instantly in the browser — no signup, no ads in your face
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Hey r/[subreddit],

I kept needing a quick pregnancy due date calculator and most options online were slow or behind paywalls, so I built one that:

• Runs 100% in your browser (your data never leaves your device)
• No signup, no email wall, no popups
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It covers the standard pregnancy due date use cases (pregnancy, due, date, baby) and links out to the formula + worked examples if you want to learn the math.

Link: https://freetoolsgalaxy.com/tools/pregnancy-due-date-calculator

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