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how to drink water more - GetMeFoodie

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 ---Question: A museum curator is organizing a digital exhibit featuring 8 historical telescopes and 5 early microscopes. If the exhibit layout requires selecting 3 telescopes and 2 microscopes to display in a row, how many distinct arrangements are possible?

📌 Solution: We are selecting and arranging instruments for display. First, choose 3 telescopes from 8: $inom{8}{3}$. Then, choose 2 microscopes from 5: $inom{5}{2}$. After selection, arrange the 5 chosen instruments in a row: $5!$ ways.

📌 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: $inom{10}{5}$.

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