+738 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
+118673 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
+118673 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
