Eight cars, each of a different color (red, blue, black, grey, white, green, tan, gold), travel one behind the other to a campground, The red car must lead and the green car must be last. How many different orderings of the cars are there?

I know that you do combinations for this but I'm not sure how to do it with the red and green car.

1 Answer
Apr 23, 2018

720

Explanation:

Ignore the red and green car as they must be first and last. This leaves six cars to place. When doing lists like this you do :
#6xx5xx4xx3xx2xx1#=6! (6 factorial)=720

The basic premise is all six could go directly behind the red car, but once one of them is there, there are only five cars to go in the next slot and so on.