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war of independence 1812 - Malaeb

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 So the number of sequences containing at least one of each module is:

📌 Question: A research team combining robotics and psychology designs a decision task where a participant chooses one of 3 cognitive strategies and one of 5 behavioral response patterns per trial. If they run 4 independent trials and require that each strategy and each response pattern is used at least once, how many valid outcome sequences are there?

📌 However, since there are 4 trials and 5 behavioral patterns, its impossible to use all 5 patterns. The maximum distinct patterns possible is 4. Therefore, the condition each behavioral response pattern is used at least once cannot be satisfied. Hence, no valid sequence exists that meets the requirement.

📌 Question: A tech startup incubator receives applications from 12 teams, of which 5 focus on AI, 4 on clean energy, and 3 on biomedical engineering. The investor plans to fund exactly 5 teams, requiring at least one from each category. How many such funding combinations are possible?

📌 Solution: We compute the total number of ways to choose 5 teams with at least one from each of the three categories. Use inclusion-exclusion over the prohibited cases.

📌 Subtract selections missing at least one category.

📌 Now add back those missing two categories (since subtracted twice):

📌 Question: A science museum exhibit features a puzzle where a visitor generates a 6-dig

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