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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 But note: for each such pair, $(x,y)$ is uniquely determined, and all are distinct. So total number is $30$.

📌 Thus, there are $30$ lattice points.

📌 Solution: We are tasked with finding the number of unique test combinations consisting of 3 distinct viral strains chosen from 7 and 2 antiviral compounds chosen from 8. Since the choices are independent, we compute the product of the combinations:

📌 Question: A science policy advisor is organizing a roundtable discussion involving 5 scientists and 3 government representatives. If the table is circular and all individuals are distinguishable, in how many distinct arrangements can they be seated such that no two government representatives are adjacent?

📌 Solution: First, fix one scientist at a seat to eliminate rotational symmetry in circular permutations. This leaves 4 scientists to arrange in the remaining seats, which can be done in $4!$ ways.

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