$(15$p$.)$ On average $40$customer groups$$ come to a coffee restaurant in one hour. Fifty percent of groups have a group size of one $($so$,$ in fact, they are single$).$ One$-$fourth of the groups are couples. The other one$-$fourth have a group size of $3.$

a$.$Find the expected number of customers coming in $30$ minutes.

b$.$Find the probability that a couple comes before a single person.

c$.$Find the probability that no couple comes in $5$ minutes.