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Home » Calculate: 70 + 86 + 102 + 118 + 134 - Appfinity Technologies

Calculate: 70 + 86 + 102 + 118 + 134 - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Total number of unrestricted arrangements of 5 distinct rituals: \(5! = 120\)

📌 Now subtract the number of arrangements where R1 and R2 are consecutive.

📌 Treat R1 and R2 as a single block. Then we have 4 units to permute: the block and the other 3 rituals.

📌 Number of ways: \(4! = 24\), and within the block, R1 and R2 can appear as (R1,R2) or (R2,R1): 2 ways.

📌 So total invalid arrangements: \(24 \times 2 = 48\)

📌 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?

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