如何计算Combinations with Replacement

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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)!)

分步指南

1. 1Unlike regular combinations, you can pick the same item multiple times
2. 2Order still does not matter (unlike permutations)
3. 3Formula: C(n+k-1, k) where n = types, k = selections
4. 4Example: Choosing 3 scoops from 5 ice cream flavors (can repeat) = C(7,3) = 35

例题解析