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why do i wake up with a headache - RoadRUNNER Motorcycle Touring & Travel Magazine

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 Question: A genetic modification researcher is testing 4 genetically edited maize varieties under drought conditions and 6 conventional varieties. If 5 varieties are selected at random for a large-scale field trial, what is the probability that exactly 2 of the selected varieties are genetically edited?

📌 Solution: Total number of ways to choose 5 varieties from 10: $inom{10}{5}$.

📌 Number of favorable outcomes: choose 2 edited from 4 and 3 conventional from 6: $inom{4}{2} \cdot inom{6}{3}$.

📌 inom{4}{2} = rac{4 \cdot 3}{2 \cdot 1} = 6

📌 inom{6}{3} = rac{6 \cdot 5 \cdot 4}{3 \cdot 2 \cdot 1} = 20

📌 inom{10}{5} = rac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 252

📌 Favorable outcomes: $6 \cdot 20 = 120$.

📌 Probability: $rac{120}{252} = rac{10}{21}$.

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