22. A laundry has six washing machines which breakdown randomly and the average time interval between successive breakdowns is 4 hours. The machines breaking down require, on an average, forty-five minutes to repair, the service time being exponentially distributed. Using this information, you are required to determine:

(a) the probabilities of 0, 1, 2, 3, 4, 5 and 6 machines in the system,

(b) the expected waiting time of a machine in the queue,

(

c) the expected number of machines in the system, and

(

d) the expected number of machines in the queue.