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Home » You Won’t Believe the Legend Behind Kabuto Yakushi—An Icon Left Undiscovered! - SUpost

You Won’t Believe the Legend Behind Kabuto Yakushi—An Icon Left Undiscovered! - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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📌 Question: An entomologist is studying a population of 12 bees, selecting a sample of 5 for genetic analysis. Among the bees, 4 are tagged for tracking, and we want to ensure at least one tagged bee is included in the sample. How many such samples are possible?

📌 Solution: The total number of ways to choose 5 bees from 12 is:

📌 The number of samples with no tagged bees (i.e., all from the 8 untagged bees) is:

📌 Therefore, the number of samples with at least one tagged bee is:

📌 Question: A robotics engineer is programming a robot to execute sequences of 8 actions, where 3 are grasp, 3 are move, and 2 are scan, all indistinct within their type. How many distinct action sequences can the robot perform?

📌 Solution: This is a multinomial coefficient problem. We are arranging 8 actions where 3 are of one kind, 3 of another, and 2 of a third, all indistinct within types. The number of distinct sequences is:

📌 Question: A UI designer is assigning 6 different color themes to 3 identical layout palettes, with each palette receiving at least one theme. How many ways can the themes be distributed across the palettes, considering palettes are indistinguishable?

📌 Solution: We seek the number of ways to partition 6 distinguishable themes into 3 non-empty, unlabeled subsets. This is given by the Stirling number of the second kind $S(6, 3)$. From known values:

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