Refer to the Journal of Transportation Engineering (May, 2013) investigation of the assignment of tracks to trains at a busy railroad station, Exercise 2.8 (p. 28). Ideally, engineers will assign trains to tracks in order to minimize waiting time and bottlenecks. Assume there are 10 tracks at the railroad station and the trains will be randomly assigned to a track. Suppose that in a single day there are 50 trains that require track assignment.
a. What is the probability that exactly 5 trains are assigned to each of the 10 tracks?
b. A track is considered underutilized if fewer than 2 trains are assigned to the track during the day. Find the probability that Track #1 is underutilized.