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Home » \binom62 + \binom63 + \binom64 + \binom65 - Crosslake

\binom62 + \binom63 + \binom64 + \binom65 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 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...
Solution: We seek the number of distinct permutations of a multiset: 1...
\frac{10!}{5! \cdot 3! \cdot 2!}
Compute:
10! = 3628800,\quad 5! = 120,\quad 3! = 6,\quad 2! = 2
\frac{3628800}{120 \cdot 6 \cdot 2} = \frac{3628800}{1440} = 2520
Thus, the number of distinct activation orders is $\boxed{2520}$.

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