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warm places to visit in december - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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:

📌 ways. Therefore, the total number of distinct arrangements is:

📌 4! \times 5! = 24 \times 120 = 2880

📌 Thus, the final answer is:

📌 \boxed{2880}

📌 A fair six-sided die is rolled three times. What is the probability that exactly two of the rolls show a number greater than 4?

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