Combinations Calculator

Count the ways to choose r items out of n when order doesn’t matter, like lottery numbers or a committee.

Whole numbers up to 1,000.
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Combinations
Exact value
Odds of one specific pick
Permutations (order matters)
Formula
Work

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Combination Formulas

Without repetition: nCr = n! ÷ (r! (n − r)!)
With repetition: (n + r − 1)! ÷ (r! (n − 1)!)

Combinations count selections where order doesn’t matter. Each combination of r items can be arranged r! ways, so nPr = nCr × r!.

Worked Example

Tips

Choosing r is the same as leaving out n − r, so C(49, 6) = C(49, 43). These are the numbers in Pascal’s triangle.