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Home » 20k \equiv 40 \pmod100 \implies k \equiv 2 \pmod5 - DNSFLEX

20k \equiv 40 \pmod100 \implies k \equiv 2 \pmod5 - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \boxed{\frac{2}{5}}

📌 Question: A health data analyst is organizing a roundtable discussion with 5 healthcare professionals and 3 public health officials. If all participants are distinguishable, in how many ways can they be seated around a circular table if the public health officials must sit together?

📌 Since the table is circular and the public health officials must sit together, we treat the group of 3 officials as a single "block." This reduces the problem to arranging 6 entities (5 professionals + 1 block) around a circular table.

📌 For circular arrangements of $ n $ objects, the number of distinct arrangements is $ (n-1)! $. So, the number of ways to arrange the 6 entities is:

📌 Within the block, the 3 public health officials can be arranged among themselves in $ 3! = 6 $ ways.

📌 Thus, the total number of arrangements is:

📌 \times 6 = 720

📌 \boxed{720}

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