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y = \frac12-4 = -3 - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \mathbb{E}[\text{output}] = \frac{1304}{256} = \frac{163}{32} \approx 5.09375

📌 Thus, the expected output is $\boxed{\dfrac{163}{32}}$.

📌 Question: A virologist is studying a viral strain with 6 distinct surface proteins. She wants to test combinations of exactly 4 proteins in a test panel, but due to safety protocols, two specific proteins (P1 and P2) cannot be tested together. How many valid 4-protein test panels can she form?

📌 Solution: Total number of 4-protein combinations from 6 proteins: $ \binom{6}{4} = 15 $

📌 Now subtract the number of panels that include both P1 and P2.

📌 If both P1 and P2 are included, we need to choose 2 more proteins from the remaining 4 (since 6 - 2 = 4).

📌 Number of such invalid panels: $ \binom{4}{2} = 6 $

📌 Therefore, number of valid panels is:

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