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Home » \( 21,250 \times 0.85 = 18,062.50 \) - AMAZONAWS

\( 21,250 \times 0.85 = 18,062.50 \) - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 We model this as placing 3 active (A) subsystems and 5 inactive (I) subsystems in a line of 8 positions, such that no two A’s are adjacent.

📌 To ensure no two A’s are adjacent, first place the 5 inactive subsystems:

📌 This creates 6 possible "gaps" where active subsystems can be placed: before, between, and after the I’s:

📌 \_ I \_ I \_ I \_ I \_ I \_ → 6 gaps

📌 We need to choose 3 of these 6 gaps to place one A each, with no two A’s in the same gap (ensuring non-adjacency).

📌 Number of ways: \(\binom{6}{3} = 20\)

📌 Each such choice gives a unique valid configuration.

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