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Home » 3rd term: \(15 \times 3 = 45\) - Portal da AcÃºstica

3rd term: \(15 \times 3 = 45\) - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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

📌 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

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