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Home » \( r = \sqrt[3]144 \approx 5.24 \) cm. - Groen Casting

\( r = \sqrt[3]144 \approx 5.24 \) cm. - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 rac{84}{210} = rac{2}{5}

📌 Therefore, the probability is $ oxed{rac{2}{5}} $.

📌 Question: A linguist analyzing word evolution models a simplified language where each word is a sequence of 8 characters, each chosen independently from the set $\{a, b, c\}$. What is the probability that a randomly generated word contains exactly 3 $a$âs, 2 $b$âs, and 3 $c$âs?

📌 Solution: This is a multinomial probability. Let $ X = (X_a, X_b, X_c) $ be the counts of each letter in a random 8-character word, with each character independently chosen from $\{a, b, c\}$ with equal probability $ rac{1}{3} $.

📌 P(X_a = 3, X_b = 2, X_c = 3) = rac{8!}{3! \cdot 2! \cdot 3!} \cdot \left(rac{1}{3}

📌 ight)^3 \cdot \left(rac{1}{3}

📌 ight)^2 \cdot \left(rac{1}{3}

📌 ight)^3 = rac{8!}{3! \cdot 2! \cdot 3!} \cdot \left(rac{1}{3}

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