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nj transit delays - Decision Point

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 #### 96Question: A virologist is studying 8 different antiviral compounds and 5 delivery mechanisms. How many ways can they select 3 compounds and 2 delivery mechanisms for a combined experiment?

📌 Solution: To determine the number of ways to choose 3 compounds from 8 and 2 delivery mechanisms from 5, we use combinations:

📌 Question: A mathematician is applying algebraic topology to analyze data clusters. If there are 12 data points and each point can be assigned to one of 4 distinct topological classes, how many distinct assignments are possible?

📌 Solution: Each of the 12 data points has 4 independent choices (topological classes). Since the assignments are independent, the total number of assignments is:

📌 Question: A circular table is to be used for a virology symposium with 5 researchers and 3 industry representatives. If all individuals are distinguishable, how many distinct seating arrangements are possible around the table, assuming rotations are considered the same?

📌 Solution: When arranging $ n $ distinguishable people around a circular table, the number of distinct arrangements is $ (n-1)! $, due to rotational symmetry.

📌 Here, there are $ 5 + 3 = 8 $ people total, so:

📌 So total number of 3-element subsets:

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