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Home » Question: What is the base-ten number represented by the base-eight number 315? - High Altitude Science

Question: What is the base-ten number represented by the base-eight number 315? - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Thus, the robot can produce $\boxed{30}$ valid sequences.

📌 Question: A virologist is analyzing a synthetic virus with a genome composed of 8 nucleotide segments, each of which can be one of four types: A, U, C, or G. She is particularly interested in configurations where exactly 3 segments are adenine (A), and no two adenine segments are adjacent. How many such valid genome sequences are possible?

📌 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.

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