A cafeteria can seat a maximum of 50 persons. Customers arrive in a Poisson stream at the rate of 10 per hour and are served (one at a time) at the rate of 12 per hour.

(a) What is the probability that an arriving 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 can be fulfilled?

(Assume that arrangements can be made to seat them together as long as three seats are available.)