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Home » Finding a common denominator, we get \(\frac2d120 + \frac3d120 = 5\). - Dachbleche24

Finding a common denominator, we get \(\frac2d120 + \frac3d120 = 5\). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 inom{8}{3} = rac{8 \cdot 7 \cdot 6}{3 \cdot 2 \cdot 1} = 56

📌 inom{5}{2} = rac{5 \cdot 4}{2 \cdot 1} = 10

📌 Total arrangements: $56 \cdot 10 \cdot 120 = 67200$.

📌 Thus, the number of distinct arrangements is $oxed{67200}$.

📌 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

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