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A barbershop serves one customer at a time and provides four seats for waiting customers. If the place is full, customers go elsewhere. Arrivals occur according to a Poisson distribution with mean five per hour. The time to get a haircut is exponential with mean 12 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.
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