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Home » Now, subtract the number of arrangements where the two N's are adjacent. - Carbonext

Now, subtract the number of arrangements where the two N's are adjacent. - Carbonext

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 Question: A historian of science is organizing a panel with 3 experts selected from a list of 6 historians, 5 scientists, and 4 physicians. What is the probability that the panel includes at least one expert from each profession?

📌 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

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