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 $(5,7)$?

Respuesta :

You need to know the number of routes that could get Marvin to 5,7, and the number that could get him to 4,3. Then take one from the other.So, to get to 5,7 Marvin make 5 steps right and 7 in any order. Similarly to get to 4,3 he does 4 right and 3 up.in any order.Now, think of a right step as a red counter and an up step as a blue counter. How many ways are they to rearrange 5 red counter and 7 blue ones?I'd I had 2 red and 3 blue I'd do 5!/2!3!….There you go, I've started you off