Combination Calculator (nCr)
Count the ways to choose r items from n when order does not matter.
Combinations (nCr)
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Formula
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Ordered arrangements (nPr)
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Results update as you type.
About this calculator
A combination counts how many ways you can choose r items from a set of n, ignoring order. The formula is nCr = n! / (r! (n − r)!). Combinations are used for lotteries, card hands and sampling. This calculator returns the exact value for large inputs.
Frequently asked questions
What is the combination formula?
nCr = n! / (r! × (n − r)!). For 10 items taken 3 at a time: 120 different groups.
Why is nCr smaller than nPr?
Combinations ignore order, so each unordered group corresponds to r! ordered permutations. That is why nCr = nPr ÷ r!.
Results are estimates for general guidance only, not financial, medical or tax advice.