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Home » Value at end of second year: \(80 + 24 = 104\) - jntua results

Value at end of second year: \(80 + 24 = 104\) - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \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}

📌 This means $ n = 7k + 3 $ for some integer $ k $.

📌 We want $ 1 \leq 7k + 3 \leq 100 $.

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