ight)^2 \cdot \left(rac{1}{3}

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• 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)^3 = rac{8!}{3! \cdot 2! \cdot 3!} \cdot \left(rac{1}{3}
• ight)^8
• rac{8!}{3! \cdot 2! \cdot 3!} = rac{40320}{6 \cdot 2 \cdot 6} = rac{40320}{72} = 560

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