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Home » From Plumber to Legend: The Hidden Secrets of Every Mario Bros Character! - AMAZONAWS

From Plumber to Legend: The Hidden Secrets of Every Mario Bros Character! - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 Thus, the probability that the significant instrument is selected is:

📌 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}

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For $n = 10$:
\sum_{k=1}^{10} k^3 = \left(rac{10 \cdot 11}{2}
ight)^2 = (55)^2 = 3025.
Now compute $3025 \mod 9$. Use the digit sum method:
Digit sum of $3025$: $3 + 0 + 2 + 5 = 10$, then $1 + 0 = 1$, so $3025...
Alternatively, divide: $3025 \div 9 = 336 imes 9 = 3024$, remainder $...
Thus, the remainder is $1$.
Therefore, the answer is $oxed{1}$.
Question: What is the greatest common divisor of $3^{15} - 1$ and $3^9...
Solution: Use the property:

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