$($c$)$ Dom & Derry Car Wash $($DDCW$)$ is the only car wash in a small town. A relatively large

number of people who live in the town are their customers. The customers arrive following a

Poisson distribution at an average of twelve car wash customers per hour. Dom and Derry

worked as a team in one of the car washing bays. As the demand is relatively high, they

decided to utilize the two other car washing bays that they have. They hired four more workers

to make two more teams. Cars wait in a single waiting line and follow an FCFS queue

discipline until one of the three teams at DDCW can serve them. Service times are distributed

exponentially; Dom and Derry spend an average of $12$ minutes per car wash, and the other

two teams spend the same for a car wash.

$($c$-1)$ How many car wash customer$/$s would they expect to serve at DDCW on average?

$($c$-2)$ What is the average time in minutes a car wash customer will spend in the DDCW

$($c$-3)$ What is the probability that a car wash customer arriving at the DDCW will immediately be

served?