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📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Let $ f(n,k) $ be the number of ways to place $ k $ non-adjacent red markers in $ n $ positions in a line.

📌 We need $ f(6,3) $ with no two reds adjacent.

📌 Check manually: list all binary strings of length 6 with exactly three 1s (red), no two adjacent.

📌 Such configurations must have at least one blue between reds. So min spacing: R-B-R-B-R, requires 5 positions. We have 6, so one extra red to place.

📌 Start with the base: R-B-R-B-R, and have one extra R to place in the 4 possible gaps: before first, between, or after last.

📌 Actually, the standard transformation: place 3 reds with at least one blue between, using stars and bars with spacing.

📌 Thus, number of favorable outcomes: 4

📌 ---Question: A 5 cm by 12 cm rectangular support beam is placed inside a circular pipeline. What is the circumference of the pipeline?

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