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 (4,4) there is a frog that will eat him if he goes through that point. In how many ways can Marvin reach (5,7)?
+2666 There are \({5 + 7 \choose 5} = 792\) ways to get from the origin to \((5,7)\)
Now, we need to subtract this from the number of ways to get form the origin to \((4,4)\).
There are \({4 + 4 \choose 4} = 70\) ways to get from the origin to \((4,4)\).
So, there are \(792 - 70 = \color{brown}\boxed{722}\) ways.
Here is a link that explains this better: https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/
+2666 There are \({5 + 7 \choose 5} = 792\) ways to get from the origin to \((5,7)\)
Now, we need to subtract this from the number of ways to get form the origin to \((4,4)\).
There are \({4 + 4 \choose 4} = 70\) ways to get from the origin to \((4,4)\).
So, there are \(792 - 70 = \color{brown}\boxed{722}\) ways.
Here is a link that explains this better: https://betterexplained.com/articles/navigate-a-grid-using-combinations-and-permutations/
