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Home » ÷ 18 = 27.5 → not - AIKO, infinite ways to autonomy.

÷ 18 = 27.5 → not - AIKO, infinite ways to autonomy.

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Question: A historian is analyzing three randomly selected scientific papers from a collection of 12, where 5 are written by Newton and 7 by Leibniz. What is the probability that exactly two of the selected papers are by Newton?

📌 Solution: The total number of ways to choose 3 papers from 12 is:

📌 \binom{12}{3} = 220

📌 To choose exactly 2 papers by Newton and 1 by Leibniz:

📌 \binom{5}{2} \cdot \binom{7}{1} = 10 \cdot 7 = 70

📌 \frac{70}{220} = \frac{7}{22}

📌 \boxed{\frac{7}{22}}

📌 Question: A geotechnical engineer is testing soil samples from 10 different sites, each labeled from 1 to 10. If 3 sites are selected at random for detailed analysis, what is the probability that site 7 is included?

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