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Home » #### \(72x^7y^18\) - Blask

#### \(72x^7y^18\) - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 2Question: A digital health solutions architect is designing a system that logs patient check-ins in real-time across multiple rural clinics. If the system must assign each patient ID uniquely using a 6-digit code where each digit is from 1 to 9 (no zeros), and no digit is repeated in any code, how many distinct check-in codes can be generated?

📌 Solution: To determine the number of distinct 6-digit codes using digits from 1 to 9 with no repetition, we calculate the number of permutations of 9 digits taken 6 at a time:

📌 P(9, 6) = \frac{9!}{(9 - 6)!} = \frac{9!}{3!}

📌 9! = 362880,\quad 3! = 6

📌 \frac{362880}{6} = 60480

📌 Thus, the total number of unique check-in codes is $\boxed{60480}$.

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