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📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 Thus, the number of 5-digit integers where each digit appears at least once is:

📌 - 93 = 150

📌 Therefore, the final answer is:

📌 \boxed{150}

📌 In a circular arrangement, 5 scientists and 4 engineers are seated around a table. If all scientists must sit together, in how many distinct ways can they be seated?

📌 First, treat the group of 5 scientists as a single "block." In a circular arrangement, the number of distinct ways to arrange \( n \) objects is \((n-1)!\). Here, we have the "block" of scientists and 4 engineers, making 5 objects in total:

📌 Within the "block," the 5 scientists can be arranged among themselves in:

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