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Combination Calculator
Calculate the number of ways to choose r items from n when order does not matter
About this calculator
A combination counts selections where order does not matter. C(n,r) = n! / (r! × (n−r)!). Choosing 3 people from 10 for a committee: C(10,3) = 120. This is also written as 'n choose r' or the binomial coefficient. Used in probability, statistics, and counting problems.
How to use
C(6,2): choosing 2 from 6. 6!/(2!×4!) = (6×5)/(2×1) = 15. There are 15 ways to pick a pair from 6 people.
Frequently asked questions
Why is C(n,r) = C(n, n−r)?
Choosing which r items to include is equivalent to choosing which n−r items to exclude. C(10,3) = C(10,7) = 120.
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.