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Home » \(n(n+1) = 10100\). - Get link 4share

\(n(n+1) = 10100\). - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Probability for one non-prime: $\frac{1}{2}$

📌 So, probability for each configuration is $\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$

📌 \times \frac{1}{8} = \frac{3}{8}

📌 Thus, the probability is $\boxed{\dfrac{3}{8}}$.

📌 Question: A science administrator reviews 5 distinct climate research proposals and must assign them to 3 indistinguishable review panels, with no panel left empty. How many ways can the proposals be distributed?

📌 Solution: We are partitioning $5$ distinguishable objects (proposals) into $3$ indistinguishable, non-empty subsets (panels). This is given by the Stirling numbers of the second kind, denoted $S(5,3)$.

📌 The value of $S(5,3)$ is computed as follows:

📌 We use the recurrence: $S(n,k) = k \cdot S(n-1,k) + S(n-1,k-1)$

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