Combinations Calculator
Combinations (nCr)
How many ways to choose r items from n (order doesn't matter)
Permutations (nPr)
How many ways to arrange r items from n (order matters)
Combinations with Repetition
Choose r items from n types with repetition allowed
Formula
C(n,r) = n! / (r!(n-r)!) | P(n,r) = n! / (n-r)! | Multiset: C(n+r-1, r)
Frequently Asked Questions
What is the difference between combinations and permutations?
Combinations: order doesn't matter (choosing a committee of 3 from 10 people). Permutations: order matters (assigning 1st, 2nd, 3rd place). C(n,r) = n!/(r!(n-r)!) while P(n,r) = n!/(n-r)!. P(n,r) = C(n,r) × r!.
What does 'n choose r' mean?
'n choose r' or C(n,r) counts the number of ways to select r items from n distinct items without regard to order. For example, C(5,2) = 10 means there are 10 ways to choose 2 items from 5.
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