A barbershop serves one customer at a time and provides three seats for waiting customers. If the place is full, customers go elsewhere. Arrivals occur according to a Poisson distribution with mean four per hour. The time to get a haircut is exponential with mean 15 minutes. Determine the following:

(a) The steady-state probabilities.

(b) The expected number of customers in the shop.

(c) The probability that customers will go elsewhere because the shop is full.