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Home » Subtract (ii) from (iii): - ClickBalance

Subtract (ii) from (iii): - ClickBalance

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 S(4,1) + S(4,2) = 1 + 7 = 8

📌 Thus, the number of distinct configurations is $\boxed{8}$.

📌 Question: A science administrator evaluates 6 unique grant proposals and wishes to distribute them into 3 identical review teams, with each team receiving at least one proposal. How many ways can this be done?

📌 Solution: We are partitioning $6$ distinguishable objects (proposals) into $3$ non-empty, indistinct subsets (teams). This is given by the Stirling number of the second kind $S(6,3)$.

📌 We compute $S(6,3)$ using recurrence:

📌 $S(6,3) = 3 \cdot S(5,3) + S(5,2)$

📌 Now compute $S(5,2) = 2 \cdot S(4,2) + S(4,1) = 2 \cdot 7 + 1 = 14 + 1 = 15$

📌 S(6,3) = 3 \cdot 25 + 15 = 75 + 15 = 90

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