Combinations Calculator
C(n,r) — order does not matter
Combinations with replacement (also called multiset coefficients) count the number of ways to choose k items from n types when you can repeat items and order does not matter. Formula: C(n+k-1, k) = (n+k-1)! / (k!(n-1)!)
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Pro Tip
Think of it as distributing k identical balls into n distinct bins: how many distributions are possible? The formula C(n+k-1, k) gives the answer.
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Did You Know?
Combinations with replacement appear in number theory as 'stars and bars' problems, in physics for counting quantum states of identical particles (bosons), and in combinatorics textbooks as the 'ice cream flavor' problem.
References
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