Mack the bug starts at (0,0) at noon and each minute moves one unit right or one unit up. He is trying to get to the point (5,7). However, at (4,3) there is a spider that will eat him if he goes through that point. In how many ways can Mack reach (5,7)?
Though I have seen other posts on this, I'm confused on how to solve the problem. I tried implementing the strategy that was used when when there was a spider at (2,3), on this one at (4,3). I want to understand this problem.
+118608 Mack the bug starts at (0,0) at noon and each minute moves one unit right or one unit up. He is trying to get to the point (5,7). However, at (4,3) there is a spider that will eat him if he goes through that point. In how many ways can Mack reach (5,7)?
I get 617 ways. Can you please confirm if you think this is correct or not.
If you believe you know the answer then please state what it is.
Here is an outline of my logic.
There are 35 ways to get from (0,0) to (4,3)
There are 5 ways to get from (4,3) to (5,7)
So there are 35*3=175 ways to get from (0,0) to (5,7) passing through (4,3)
There are 792 ways to get from (0,0) to (5,7)
So there must be 792-175=617 ways to get from (0,0) to (5,7) without passing through (4,3)
My logic seems ok to me.
