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Home » x = \frac11.68 = 1.45 - Feedz API

x = \frac11.68 = 1.45 - Feedz API

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 Question: In a futuristic city, 7 autonomous taxis and 5 delivery drones are to be stationed at 12 distinct pickup points, with each point assigned to exactly one vehicle. How many ways can they be assigned if taxis and drones are distinguishable but pickup points are indistinct in function (only assignment matters)?

📌 We are assigning 12 distinct pickup points to 7 distinguishable taxis and 5 distinguishable drones, with each point assigned to exactly one vehicle. Since vehicles are distinguishable and each gets a unique point (no shared points), this is equivalent to partitioning the 12 distinct points into 7 labeled groups (taxis) and 5 labeled groups (drones), with no overlap.

📌 This is the number of ways to assign 12 distinct items to 12 distinct positions across labeled categories (7 taxis, 5 drones), where each position gets exactly one vehicle. Since the vehicles are labeled and each gets a unique pickup point, this is simply:

📌 Because we assign each of the 12 distinct pickup points to one of the 12 distinct roles (7 taxis, 5 drones), and the order matters via labeling.

📌 Thus, the number of assignment configurations is:

📌 Then, the number of signal-induced responses is:

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