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Home » You WON’T BELIEVE What Happened When Rigby Plus Regular Show Joined Forces! - Sterling Industries

You WON’T BELIEVE What Happened When Rigby Plus Regular Show Joined Forces! - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Question: A mathematician working with topological data analysis considers a simplicial complex built from 7 labeled data points. How many distinct non-empty subsets of these points can form a 2-simplex (triangle), assuming any three points form a simplex?

📌 Solution: A 2-simplex is uniquely determined by any 3 distinct points, since all triangles are allowed. The number of ways to choose 3 points from 7 is:

📌 Each such subset forms a valid 2-simplex, and all are non-empty and distinct. Thus, the number of distinct 2-simplices (triangles) is $35$.

📌 Question: A science policy advisor is organizing a roundtable discussion with 8 scientists from 3 different disciplines: 3 physicists, 3 chemists, and 2 biologists. If scientists of the same discipline are indistinguishable in seating labeling, how many distinct seating arrangements are possible around a circular table?

📌 Now divide by 8 for rotational symmetry in circular arrangements:

📌 Thus, there are $70$ distinct seating arrangements.

📌 Question: An industrial designer offers custom phone cases with 5 color palettes and 4 pattern options. A customer picks exactly 3 different colors and 1 pattern, where the order of colors does not matter. How many unique case designs can be made?

📌 Solution: First, choose 3 different colors from 5, where order does not matter:

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