A Multi-Service Center has space for four people: two receiving care from two specialists and two waiting for an appointment. When there are four clients, other clients are not allowed to enter and the shifts are attended to on a first-come, first-served basis. The arrival of customers to the system follows a Poisson distribution at a rate of 30 customers per day and the service time follows an exponential distribution with an average of 5 min per customer. We wish to determine:

(a) The probability that when a customer arrives, he/she does not have to wait.

b) The probability that a customer arrives and finds that there is one customer waiting.

c) The average number of customers in the Multiservice center.

d) The time that a customer stays in the Multiservice center.

e) The probability that a customer arrives at the Multiservice center and cannot get in.