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Home » Outer: \( 3x \times 5 = 15x \). - Dachbleche24

Outer: \( 3x \times 5 = 15x \). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 \frac{3628800}{24 \cdot 120 \cdot 1} = \frac{3628800}{2880} = 1260

📌 Thus, the number of unique activation sequences is $\boxed{1260}$.

📌 \boxed{1260}

📌 Question: A startup uses a rotation-based irrigation system activated by 5 identical solar valves, 3 identical pressure regulators, and 2 identical flow meters. If each component is engaged once over 10 days, how many distinct activation orders exist?

📌 Solution: We seek the number of distinct permutations of a multiset: 10 components — 5 identical solar valves (V), 3 identical pressure regulators (P), and 2 identical flow meters (F). The total number of sequences is:

📌 \frac{10!}{5! \cdot 3! \cdot 2!}

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

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