Seating arrangement

Probability Level 2

Archimedes, Pythagoras, Marvin, Euler, Leibniz, and Descartes are seated at random around a table. This table is in the shape of regular hexagon. Each side of the table has one person each. What is the probability that Marvin and Pythagoras are seated opposite each other?

1 6 \frac{1}{6} 1 5 \frac{1}{5} 1 3 \frac{1}{3} 1 7 \frac{1}{7} 1 4 \frac{1}{4}

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1 solution

Oliver Papillo
Jan 1, 2017

Ignoring the other four positions, there are 5 5 possible choices for who is sitting across from Marvin, and they are all equally likely.

Therefore the chance that Pythagoras is sitting across from Marvin is 1 5 \frac{1}{5} .

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