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(151)   (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
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