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Home » Inside the Ultimate Western Women Boot That Every Fashion-Focused Shopper Needs - Decision Point

Inside the Ultimate Western Women Boot That Every Fashion-Focused Shopper Needs - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Thus, valid arrangements: \(120 - 48 = 72\)

📌 So the answer is \(\boxed{72}\)

📌 An electrical engineer designs a smart grid system with 8 distinct subsystems, each capable of being in one of two states: active or inactive. How many configurations exist such that exactly 3 subsystems are active, and no two active subsystems are adjacent?

📌 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

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