Marvin the fly starts at \((0,0)\). Each step, Marvin 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 frog that will eat him if he goes through that point. In how many ways can Marvin reach \((5,7)\)?

I tried 757, but it wasn't right.

This is what I tried:

\(\frac{(5+7)!}{5!*7!}\)= 792 paths to (5,7).

\(\frac{(4+3)!}{4!*3!}\)= 35 paths to subtract.

792-35=757. But I guess that wasn't right.

Please help!

thank you!!! :D

lokiisnotdead Apr 20, 2020

edited by
lokiisnotdead
Apr 20, 2020

edited by lokiisnotdead Apr 20, 2020

edited by lokiisnotdead Apr 20, 2020

edited by lokiisnotdead Apr 20, 2020

edited by lokiisnotdead Apr 20, 2020

#3**+2 **

Total possibilities with no restrictions

12 steps altogether. 5 are horizontal 12C5=792 just as you got

Total number that go to (4,3)

7 steps to get from start to (4,3) four are horizontal = 7C4 = 35 ways

Number of ways from (4,3) to (5,7)

5 steps, 1 horizontal = 5 ways

35*5=175 ways to get from start to finish if you go through (4,3)

Number of ways to get from start to finish if you do not go through (4,3) is 792-175 = **617**

Melody Apr 20, 2020

#3**+2 **

Best Answer

Total possibilities with no restrictions

12 steps altogether. 5 are horizontal 12C5=792 just as you got

Total number that go to (4,3)

7 steps to get from start to (4,3) four are horizontal = 7C4 = 35 ways

Number of ways from (4,3) to (5,7)

5 steps, 1 horizontal = 5 ways

35*5=175 ways to get from start to finish if you go through (4,3)

Number of ways to get from start to finish if you do not go through (4,3) is 792-175 = **617**

Melody Apr 20, 2020