A popular dancing club has the capacity of $10$ people. If it is full, a newly arrived person waits in front

of the door of the club. Each person dances $1$ hour on average. The mean time between arrivals is $20$ minutes.

a$.$ Is this queue stable? If so$,$ solve below questions.

b$.$ Find the probability that the club will be full in steady$-$state.

c$.$ Find the probability that the queue will be longer than $5$ in steady$-$state.

d$.$ Find the probability that a person will wait more than $10$ minutes in the queue.