Question 35
Five friends must get off a five-seat chairlift and can go in three different directions: left, straight ahead or right. When getting off a chairlift it is easy to collide with fellow passengers. For example, if I decide to go straight and someone to my left goes right, we collide; the same happens if I go right and someone to my right goes straight (or left). If someone goes in the same direction as me, we do not collide; and so on. If each of the five friends chooses a direction at random, with probability $1/3$ for each direction, what is the probability that there are no collisions?
(A) $\frac{25}{27}$
(B) $\frac35$
(C) $\frac{40}{81}$
(D) $\frac13$
(E) $\frac7{81}$
(A) $\frac{25}{27}$
(B) $\frac35$
(C) $\frac{40}{81}$
(D) $\frac13$
(E) $\frac7{81}$