Combination Calculator
Calculate C(n,r): the number of ways to choose r items from n.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter the total number of items (n) and the number to choose (r). The calculator computes C(n,r) using the formula n! / (r! * (n-r)!). Order does not matter in combinations. For large values, the calculator uses logarithmic factorials to avoid overflow.
About Combinations
Combinations count the number of ways to select items from a group where the order of selection does not matter. Choosing (A,B,C) is the same as (C,A,B). Combinations are also called binomial coefficients and appear in the binomial theorem, Pascal's triangle, and probability calculations. If order matters, use permutations instead.
Frequently Asked Questions
What is the difference between combination and permutation?
Combinations ignore order (choosing a committee). Permutations count order (arranging a lineup). C(n,r) = P(n,r) / r!. Combinations are always less than or equal to permutations.
What is C(n,0) and C(n,n)?
Both equal 1. There is exactly one way to choose nothing and exactly one way to choose everything.
Where are combinations used in real life?
Lottery odds, poker hands, committee selection, sampling, and anywhere you need to count selections where order does not matter.