Your model train has one engine and eight train cars. Find the total number of ways you can arrange the train. (The engine must be first.
The eight train cars can be arranged in 8 ! ways = 40,320 arrangements
The engine has to be first, then the eight cars can be arranged in eight factorial ways...
...unless the caboose has to be last, and then the answer is seven factorial.
8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320