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texas roadhouse veterans day vouchers - Redraw

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 $7\binom{8}{7} = 7 \cdot 8 = 56$

📌 $8\binom{8}{8} = 8 \cdot 1 = 8$

📌 Total = $280 + 280 + 168 + 56 + 8 = 792$

📌 Total numerator: $512 + 792 = 1304$

📌 \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 $

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