A train consists of $2$

first class coaches, $3$

second class coaches, $2$

dining coach and $4$

baggage coaches. We assume that the coaches of the same type cannot be distinguished.

In how many ways can the train be composed

a$)$ if the coaches of the same type have to be together?

b$)$ if the coaches of the same type have to be together and the $2$

first class coaches have to be at the beginning of the train?

c$)$ if the coaches can be arranged in any order?

d$)$ if the $2$

first class coaches have to be at the beginning of the train, but the remaining coaches can be arranged arbitrarily?