- #1
lus1450
- 40
- 1
Homework Statement
There are 7 different routes from A to B, 4 different routes from B to C, and two different routes from C to A. What are the possible routes from A to C and back, allowing any route to be traversed once in each direction.
Homework Equations
The Attempt at a Solution
So I think I have it, but I just need some verification since we've only had one lecture and my high school combinatoric lessons (if you could call them that) weren't very "in depth" and several years ago.
So I figure these are the possibilities:
A to B to C to A gives 7*4*2 = 56 possible routes
A to B to C to B to A gives 7*4*4*7 = 784 possible routes
A to C to A gives 2*2 = 4 possible routes
Altogether that makes 844 possibilities.
However, I'm wondering if this one "counts" as well:
A to B to A to C to A gives 7*4*7*2*2 = 784, however I'm not sure if that double counts some of the routes from above. Any help would be greatly appreciated.
Edit: I also just thought of A to C to B to A, but that one I think double counts. Thanks again.