00:01
So we're given this graph and we're first we're asked to find how many paths are there from a to c.
00:07
So remember a path can only hit each vertex once and each edge once.
00:14
So first we can use a to b and then using e1 and then b to c.
00:24
Since we hit b we can't go back and use e2, e3, or e4 so we have to go to c from there.
00:28
So there's one path we can go and use e2 and then we can go and use e3 and then take e5 and then e4 and then take e5.
00:39
So there's only four paths from a to c.
00:45
This is no repeated vertices or edges.
01:01
So a trail can have repeated vertices but no repeated edges.
01:05
So for this one all of our paths are already considered a trail and that's because each of our paths only used each edge one time.
01:30
So now to find the number of trails first we can go from a to b using e1 and then we can go back to a but we're not allowed to use e1.
01:49
So we can use e2 and then we can go back using e3 but from here we have to go to c because if we use e4 we're going to have to repeat an edge.
02:05
So that's one possible way and then for our that's one possible way and then instead of choosing e2 second we could have chosen e3 second and then we could have chosen e2 third or we could have chosen e4 third after that.
02:28
So this becomes a counting problem.
02:29
So what we're doing is out of these four we can select three of the edges but we can't repeat them.
02:39
So our first edge, our first edge we have four options...
