247. Six examinees. Suppose that during the exam, six students sit on one bench, with aisles on both sides. They finish the exam in a random order and leave immediately. What is the probability that someone will have to disturb one of the remaining five classmates to get to the aisle?
247. Let $n$ students be sitting on a bench. Then the probability that the first one of them to finish the exam will not have to disturb anyone when he makes his way to the aisle is obviously $\frac{2}{n}$. Therefore, the probability that someone among 6 students will have to disturb someone among the other 5 is $1-\frac{2}{6} \cdot \frac{2}{5} \cdot \frac{2}{4} \cdot \frac{2}{3}=\frac{43}{45}$.

$[$ H. Ives, A. M. M., 50, 202 (March 1943).]