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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.

 Jan 18, 2020
edited by Guest  Jan 18, 2020
 #1
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The number of ways is c(12,5) - c(7,2)*c(5,2) = 582.

 Jan 18, 2020
 #2
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Just wondering, how did you get 12,5? Maybe because of that, the answer is incorrect?

Guest Jan 18, 2020
 #4
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Are you saying that this first answer is wrong?  Why do you believe this to be the case?

You must have a reason. You should fully state it.

Melody  Jan 19, 2020
 #3
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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.

 Jan 19, 2020

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