A $8\times8$ square grid allows movement only along the left-right or up-down direction with no back tracking. If $A$ is the total number of paths from lower left corner to upper right corner and $B$ is the number of paths from lower left corner to upper right corner which do not cut the diagonal joining the two end points then find $\frac AB$
My Attempt:
$A=\frac{16!}{8!8!}$
$B=\frac A2$
So, $\frac AB=2$
But the answer given is $9$
Looks like my understanding of B is not correct.
I just thought we need to take those paths which are below the diagonal, so, half?