SOLUTION: Please help me solve the following: There are 9 ways to get from Point A to Point B. There are 8 ways to get from Point B to Point C. How many ways can you get from Point A to

Question 90821: Please help me solve the following:
There are 9 ways to get from Point A to Point B. There are 8 ways to get from Point B to Point C. How many ways can you get from Point A to Point B to Point C and back to Point A without retracing your steps? I have tried online tutoring, 9! 9!+8!, counting (which takes forever) and numerous websites. I cannot find a problem similar to this one.
Thank you
Answer by kev82(148) (Show Source):
You can put this solution on YOUR website!
Hi,

The first thing you do is go from A to B. There are 9 different paths to take, right?

Then you go from B to C and there are 8 different paths to take, right?

Now you must go back from C to B. There are eight paths, but you already travelled along one of them to get from B to C, and you can't retrace your steps, so that leaves 7 paths to choose.

Finally you must get from B back to A. There are 9 paths to use but you've already used 1, so there are 8 left that you can actually take.

So there are 9*8*7*8 which is 4032 different ways to go.

Kev