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Home » Substituting $ s = \fraca + b + h2 $, the final expression for the ratio is: - AMAZONAWS

Substituting $ s = \fraca + b + h2 $, the final expression for the ratio is: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Solution: We are to count the number of 8-segment sequences using letters A, U, C, G, such that:

📌 Exactly 3 of the segments are A,

📌 No two A’s are adjacent,

📌 The remaining 5 segments are chosen from U, C, G (each can be used any number of times, including zero), and are distinct in labeling (but not required to be unique beyond count per type).

📌 We proceed in two steps: first place the 3 A’s such that no two are adjacent, then assign non-A labels to the remaining positions.

📌 Step 1: Place 3 non-adjacent A’s in 8 positions.

📌 To place 3 non-adjacent A’s in 8 positions, we use the combinatorial method of placing k non-adjacent items in n slots.

📌 This is equivalent to placing 3 A’s and 5 non-A’s, with at least one non-A between any two A’s.

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