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Updated 2026-03-07 UTC
Combination Calculator — nCr with Examples
Compute combinations (nCr): the number of unordered selections. Includes examples, verification tips, and common mistakes — powered by GetCalcMaster.
Combinations count **unordered** selections. If order doesn’t matter (e.g., choosing a committee), you want combinations (nCr), not permutations (nPr).
Important: This content and tool are for educational purposes only. Outputs are estimates; always cross‑verify with official sources and/or a qualified professional.
What this calculator is
The Scientific Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Immediate results as you change inputs
- Transparent assumptions and explainable outputs
- Works well with the built‑in Notebook for saving scenarios
Formula
nCr = n! / (r! (n−r)!) (for integers n≥0, 0≤r≤n)Quick examples
ncr(10, 3) # 120ncr(5, 2) # 10# Symmetry check ncr(10, 3) - ncr(10, 7)
Verification tips
- Symmetry: nCr = nC(n−r).
- Edge cases: nC0 = 1 and nCn = 1.
- Relationship: nCr = nPr / r!.
Common mistakes
- Using combinations when order matters (you probably want permutations).
- Forgetting that r must be between 0 and n.
- Integer overflow for large n — use logs if you only need magnitude.
How to use it (quick steps)
- Choose n (total items) and r (items chosen).
- Open the Scientific Calculator.
- Enter ncr(n, r) to compute the number of combinations.
- Use symmetry to verify: nCr = nC(n−r).
- If order matters, use permutations (nPr) instead.
Related tools and guides
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Scientific calculator guide
Scientific workflows and key functions.
Trigonometry workflow
sin/cos/tan with unit checks.
Logarithms workflow
ln, log10, and change-of-base.
Math hub
Tools + explainers across math topics.
FAQ
What’s the difference between nCr and nPr?
nCr ignores order (combinations). nPr counts order (permutations).
Why is nC0 equal to 1?
There is exactly one way to choose nothing: choose the empty set.
How can I verify a combination result?
Use symmetry (nCr = nC(n−r)) or check against nPr/r!.
Tip: For reproducible work, save your inputs and reasoning in Notebook.