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Home » This Hidden Sanctum Sanctorum Will Shock You—What Secrets Lurk Inside?! - Crosslake

This Hidden Sanctum Sanctorum Will Shock You—What Secrets Lurk Inside?! - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \frac{12!}{5! \cdot 4! \cdot 3!}

📌 $ 12! = 479001600 $

📌 $ 5! = 120 $, $ 4! = 24 $, $ 3! = 6 $

📌 Denominator: $ 120 \cdot 24 \cdot 6 = 120 \cdot 144 = 17280 $

📌 \frac{479001600}{17280} = 27720

📌 Alternatively, step-by-step:

📌 \frac{12!}{5!4!3!} = \binom{12}{5} \cdot \binom{7}{4} \cdot \binom{3}{3} = 792 \cdot 35 \cdot 1 = 27720

📌 Thus, the number of distinct eating sequences is $ \boxed{27720} $.Question: Suppose $ v $ is a positive multiple of $ 5 $. If $ v^3 < 1700 $, what is the greatest possible value of $ v $?

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