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Home » – Exploding Kittens Card Game: The Wild Card Fights That Drifted Onto YouTube! - Sterling Industries

– Exploding Kittens Card Game: The Wild Card Fights That Drifted Onto YouTube! - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Question: A UI designer is creating a dynamic dashboard that displays 7 unique widgets, each assigned to one of 4 equivalent layout zones, where zones are indistinguishable in function and position. How many ways can the widgets be distributed among the zones if each zone must contain at least one widget?

📌 Solution: This is equivalent to partitioning 7 distinguishable widgets into 4 non-empty, unlabeled subsets. This is given by the Stirling numbers of the second kind, $S(7, 4)$, and since the zones are indistinguishable, we do not multiply by any permutation factor. From known values:

📌 Thus, there are 350 distinct ways to distribute the widgets into the indistinct zones with no empty zone.

📌 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?

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