A certain train has 10 cars that are being lined up on a track. One of the cars is the engine, and another is the caboose. The engine will be the first car in line. The caboose will be the last car in line. In how many ways can the cars be lined up?

8! Ways

Step-by-step explanation:

We have 10 cars to arrange. We already arrange 2 cars, hence, there are 8 spaces left to be filled between the engine and the caboose car.

Now the first car to be filled has 8 different choices, the next has 7 choices, the next 6 choices, the next 5 choices, the next 4 choices, the next 3 choices, the next 2 choices and the last a single choice.

Hence, to compute the number of ways in which these remaining 8 cars can be arranged, we simply compute the factorial 8! = 40,320 ways