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📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 A neural prosthetics specialist needs to design a set of 6 unique nerve-integrated robotic limbs, each with one of three possible biocompatible materials. How many ways can the specialist assign materials to the limbs if at least one limb must be made from each material?

📌 The intersection of all three sets is empty:

📌 Using inclusion-exclusion, the number of assignments using all three materials is:

📌 = 64 + 64 + 64 - 1 - 1 - 1 + 0 = 189

📌 So, the number of ways to assign materials with at least one limb for each material is:

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