Now you just need to count the number of ways that you can get to each of these points.
Note the number of paths will be symmetric for points of the form (x,y) (y,x) i.e (0,5) will be the same of (5,0).
So there is one way to you and one way for you frend to get to (0,5)
There are ways for you and for you friend to get to (1,4)
There are ways for you and for you friend to get to (2,3)
Because of the symmetry we can add all of these up to get
There are paths total