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Let total students = \( x \) - Sterling Industries

📅 April 15, 2026 👤 scraface

Apr 15, 2026

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🔥 Popular Posts

\frac{n}{n} \cdot \binom{n - k}{k} + (-1)^k \cdot \frac{n}{n - k} \cdo...
But for small $n=8$, $k=3$, we use a constructive method.
Fix one station as selected. By rotational symmetry, fix station 1. Th...
So available: 3, 4, 5, 6, 7, excluding 2 and 8 → valid: 3–7.
We need 2 non-adjacent from {3,4,5,6,7}.
List all 2-element non-adjacent pairs in 5 consecutive positions:
Total: 6 valid pairs with station 1 selected.
But each selection is counted 3 times (once for each selected station)...
\frac{8 \times 6}{3} = 16
Thus, number of non-adjacent triplets is 16.

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