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springhill suites by marriott atlanta buckhead - Network4

📅 May 19, 2026 👤 scraface

May 19, 2026

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📌 5A robotics engineer is designing a modular robot system with 5 identical arm units, 3 unique sensor arrays, and 2 backup power modules. Each complete robot must include exactly one arm, two sensor arrays, and at least one power module (either one or both). How many distinct robot configurations can be built?

📌 First, choose one arm unit: since all are identical in function but considered distinct in design, there are 5 choices.

📌 Next, choose 2 out of 3 sensor arrays: this can be done in C(3,2) = 3 ways.

📌 For power modules, we need at least one of the 2 (P1 and P2). The valid combinations are: (P1 only), (P2 only), or (P1 and P2) — a total of 2² - 1 = 3 choices.

📌 Multiply all choices: 5 × 3 × 3 = <<5*3*3=45>>45 distinct configurations.

📌 An ornithologist tracks 12 migratory birds fitted with GPS tags. Each bird follows one of three migration routes: Route A (4 birds), Route B (5 birds), or Route C (3 birds). Due to weather anomalies, birds on Route A are 1.5 times more likely to be delayed than those on Route B, and birds on Route C are twice as likely as Route B. If delays occur independently, and each route has a base delay probability p, express the expected number of delayed birds across all routes in terms of p.

📌 Let delay probability for Route B be p. Then Route A: 1.5p, Route C: 2p.

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