15-22 Cafeteria can seat a maximum of 50 persons. Customers arrive in a Poisson stream at the

rate of 10 per hour. They are serviced at the rate of 12 per hour.

a) What is the probability that the next customer will not eat in the cafeteria because it is full?

b) Suppose that three customers (with random arrival times) would like to be seated together.

What is the probability that their wish cannot be fulfilled? (Assume that arrangements can

be made to seat them together as long as there are three empty seats anywhere in the

cafeteria.)