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Home » Iggy Koopa Shocked Us All: The Ultimate Super Koopa Secret Revealed! - 500apps

Iggy Koopa Shocked Us All: The Ultimate Super Koopa Secret Revealed! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 ### 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}

📌 \boxed{\frac{24}{91}}

📌 $$Question: How many of the 100 smallest positive integers are congruent to 3 modulo 7?

📌 Solution: We are asked to count how many of the first 100 positive integers satisfy the congruence:

📌 n \equiv 3 \pmod{7}

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