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Home » Discover the Mysterious Giantess City Hidden Beneath Earth’s Surface! - AMAZONAWS

Discover the Mysterious Giantess City Hidden Beneath Earth’s Surface! - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Solution: We are given a multiset of 10 components: 3 identical sensors (S), 5 identical drones (D), and 2 identical robotic arms (R). The number of distinct activation sequences is the number of distinct permutations of a multiset. The total number of sequences is given by the multinomial coefficient:

📌 \frac{10!}{3! \cdot 5! \cdot 2!}

📌 Calculate:

📌 10! = 3628800,\quad 3! = 6,\quad 5! = 120,\quad 2! = 2

📌 \frac{3628800}{6 \cdot 120 \cdot 2} = \frac{3628800}{1440} = 2520

📌 Thus, there are 2520 distinct activation sequences.

📌 \boxed{2520}

📌 Question: An AI startup trains a model using 6 identical blue data batches, 4 identical green data batches, and 3 identical red batches. If the batches are processed one per day over 13 days, how many distinct processing orders are possible?

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