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Problem 210

Combinatorics Difficulty 1.4 Multiple choice CEMC Fermat · Canada · 2024

In a photograph, Aristotle, David, Flora, Munirah, and Pedro are
seated in a random order in a row of 55 chairs. If David is seated in the
middle of the row, what is the probability that Pedro is seated beside
him?

Pick one

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Official solution

After David is seated, there are 44 seats in which Pedro can be seated, of which 22 are next to David. Thus, the probability that Pedro is next to David is 24\frac{2}{4} or 12\frac{1}{2}.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.