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Home » \[ 5x = 5 \times 30 = 150 \] - SUpost

\[ 5x = 5 \times 30 = 150 \] - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 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?

📌 Solution: We compute the number of distinct permutations of a multiset with 13 total batches: 6 blue (B), 4 green (G), and 3 red (R). The number of sequences is:

📌 \frac{13!}{6! \cdot 4! \cdot 3!}

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