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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)!)

Hướng dẫn từng bước

  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

Ví dụ có lời giải

đầu vào
n=5 flavors, k=3 scoops (repeats allowed)
Kết quả
C(7,3) = 35 combinations
(5+3-1)! / (3! × 4!) = 35

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