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Home » 9 Pro Java Tricks: Elevate Your Programming in Minutes! - Treasure Valley Movers

9 Pro Java Tricks: Elevate Your Programming in Minutes! - Treasure Valley Movers

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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📌 We are selecting 3 experts from a total of $ 6 + 5 + 4 = 15 $ professionals.

📌 We want the probability that the 3 selected include **at least one historian, one scientist, and one physician**.

📌 ### Step 1: Total number of ways to choose 3 experts from 15:

📌 \text{Total ways} = \binom{15}{3} = 455

📌 ### Step 2: Favorable outcomes — at least one from each profession

📌 To satisfy at least one from each profession, we must have **1 historian, 1 scientist, and 1 physician**.

📌 \binom{6}{1} \cdot \binom{5}{1} \cdot \binom{4}{1} = 6 \cdot 5 \cdot 4 = 120

📌 P(\text{at least one from each profession}) = \frac{120}{455} = \frac{24}{91}

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