Combination Calculator

Solve ⁿCᵣ = n! / (r!(n − r)!) step by step — free combination calculator with worked examples, real-world defaults and instant answers.

ⁿCᵣ = n! / (r!(n − r)!)

Total items nItems chosen r

1,39,83,816

Ways to choose 6 from 49 (order ignored)

1
Count the ordered arrangements first:
49P6 = 49!/(49−6)!
2
Every group of 6 got counted 6! times (once per ordering) — divide it out:
49C6 = 49P6 / 6!
3
Result:
49C6 = 1,39,83,816
4
Symmetry check — choosing r to keep equals choosing n−r to discard:
49C6 = 49C43 ✓

The default 49C6 = 13 983 816 is the classic 6-from-49 lottery: one ticket's odds are 1 in ~14 million. Combinations power binomial probabilities, poker odds and A/B-test math — anywhere groups matter but order doesn't.

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Combinations nCr — unordered selections, Pascal's triangle entry.

About Combination Calculator

The Combination Calculator solves ⁿCᵣ = n! / (r!(n − r)!) for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. The default 49C6 = 13 983 816 is the classic 6-from-49 lottery: one ticket's odds are 1 in ~14 million.

How to use Combination Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into ⁿCᵣ = n! / (r!(n − r)!) and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Combination Calculator?

✓Solves ⁿCᵣ = n! / (r!(n − r)!) instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Combination Calculator use?+

It uses ⁿCᵣ = n! / (r!(n − r)!). The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Combination Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Combination Calculator on your website

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