http://i43.photobucket.com/albums/e3...tticePaths.jpg

Can some one please check if I am solving this problem correctly?

I am supposed to calculate the number of lattice paths from origin to pt (9,9) that avoids (2,2) (3,5) and (6,7)

The total number of possible paths from origin to (9,9) can be found out by using

C(x+y, x) = C(9+9, 9) = C(18, 9)

Lets say for the picture shown above:

1 = number of paths from origin to (2,2)

2 = number of paths from (2,2) to (3,5)

3 = # of paths from (3,5) to (6,7)

4 = # of paths from (6,7) to (9,9)

Now I will take C(18,9) - 1*2*3*4 to find out the number of lattice paths from origin to pt (9,9) that avoids (2,2) (3,5) and (6,7).

Another question I am not too sure how to find number of paths from (3,5) and (2,2) would it be C(3-2 + 5-2, 3-2) ?

Will that be correct? Thank you very much for your help!!