Calculation details
Planning estimate only, not financial, tax, or legal advice. Verify assumptions and current rules before making decisions.
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Use this result
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What does this calculator estimate?
A combinations calculator finds how many ways to choose items when order doesn't matter. Enter n and r to see nCr.
- nCr = n! ÷ (r! × (n−r)!)
- 5C3 = 10
- Order doesn't matter (vs permutations)
What combinations count
Combinations count the ways to select a group where order doesn't matter — picking a 3-person committee from 5 people, or 5 cards from 52. The factorial formula grows fast: 52C5 is nearly 2.6 million.
Limitations to watch for
The formula handles moderate numbers — huge n and r overflow practical computation (the tool uses log or iterative math). Combinations assume no repetition. If order matters, use permutations instead.
How to use it in practice
Use nCr for selections, lottery odds, and grouping problems. Compare with nPr (permutations) when order matters. For small numbers, check the math by hand: 5C3 = 10.
['Enter the total items n.', 'Enter the group size r.', 'Read the number of combinations.']
How this calculator works
Formula
nCr = n! ÷ (r! × (n − r)!) — the number of ways to choose r items from n without order mattering.
Worked example
Choosing 3 items from 5: 5C3 = 10 combinations.
Assumptions to verify
- Selection without repetition.
- Order does not matter.
- The factorial math is computed accurately.
Frequently asked questions
What is a combination?
A selection where order doesn't matter: 5C3 = 10 ways to choose 3 from 5.
How is nCr calculated?
n! ÷ (r! × (n−r)!).
What's the difference from permutations?
Permutations count ordered arrangements (5P3 = 60); combinations count unordered groups (5C3 = 10).
What are combinations used for?
Lottery odds, committees, card hands, and any 'choose a group' problem.
Can items repeat?
No — the standard formula assumes distinct items without repetition.
Why is 52C5 so large?
2,598,960 — the number of 5-card poker hands, which is why lotteries have such long odds.
Does order matter in the tool?
No — that's the definition of a combination; use the permutations tool if order matters.
Cite this tool
BoringToolsKit. “Combinations Calculator (nCr).” boringtoolskit.com/combinations-calculator/ (reviewed 2026-08-25). Free to reference in articles, syllabi, and answer posts with a link.
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