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Home » The Shocking Truth: What Nemesis Prime Is Waiting to Destroy Your World! - Coaching Toolbox

The Shocking Truth: What Nemesis Prime Is Waiting to Destroy Your World! - Coaching Toolbox

📅 May 6, 2026 👤 scraface

May 06, 2026

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📌 We apply a change of variables to convert the problem into one without adjacency constraints.

📌 Thus, 13 sequences of length 5 have no two consecutive 1s.

📌 We compute the probability that a randomly selected 4-event sequence (each C or V, uniformly and independently) has exactly two Cs and no two Cs are adjacent.

📌 We count the number of binary sequences of length 4 with exactly two 1s (representing clicks) and no two 1s adjacent.

📌 We choose 2 positions for C (1s) such that they are not adjacent.

📌 List all valid combinations of positions (0-indexed):

📌 This ensures no two adjacent durations differ by exactly 1.

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