Question

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.

Answer 1

This is called a permutation. You would solve this in the following way: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This could also be written as 8!. The answer would be 40,320. Hope this helps.

Answer 2

40,320

Explanation:

We are given that there are 8 train cars and 1 engine.

We will fix the first place for the engine.

So, we are left with 8 options for the next place.

Now, if we fix the second place for any one of the train cars.

We will be left with 7 options for the next place.

Going on this way until there is no place left for the train cars, we get the relation,

Total number of ways to arrange the train = 1 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

i.e. Total number of ways to arrange the train = 1 × 8! = 8! = 40,320

Hence, the total number of ways to arrange the train is 40,320.