A certain western state produces license plates for all the registered vehicles in the state. Each license plate contains a field with four numbers, followed by a field with $3$ letters of the alphabet. Numbers $(1$ to $9)$ are allowed to repeat; zero is allowed only in last cell of numeric field. Letters of the alphabet $(A$ to $Z)$ in alpha field must be distinct, that is$,$ letters on license plate are not allowed to repeat. Letter $"O"$ is not used by the state on license plates due to possible confusion with 'zero'.

How many different license plates can be produced by this western state? Show work! Evaluate your solution.

The owner of a dealership that sells unique vintage automobiles is planning to make a television commercial to feature his luxury vintage vehicles. Assume that the dealership has a showroom with $8$ rotating platforms of different heights on which the vehicles can be prominently displayed. The dealership has a current inventory of nineteen unique $($one$-$of$-$a$-$kind$)$ luxury vintage automobiles. The owner must select from his inventory the eight vintage vehicles that will be featured in the TV commercial, displayed on the rotating platforms in his showroom.

In how many different ways may the owner of the dealership select the vintage vehicles to feature in the TV commercial on the rotating platforms? Show work! Evaluate your solution.