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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)!)
ステップバイステップガイド
- 1Unlike regular combinations, you can pick the same item multiple times
- 2Order still does not matter (unlike permutations)
- 3Formula: C(n+k-1, k) where n = types, k = selections
- 4Example: Choosing 3 scoops from 5 ice cream flavors (can repeat) = C(7,3) = 35
解いた例
入力
n=5 flavors, k=3 scoops (repeats allowed)
結果
C(7,3) = 35 combinations
(5+3-1)! / (3! × 4!) = 35
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