A particle moves only towards above or towards right in each step. For $a, b, c, d, m \in \mathbb{Z}$, calculate the number of possible paths from the point $(a, b)$ to $(c, d)$ which do not touch or cut the line $y = m$, where $b < m < d$.
I am stuck with the last property that's given, which is that $b < m < d$. Given that we can't cross $y=m$, this makes it impossible.
For example, take $(a,b)=(1,2)$, $y=4$, $(c,d)= (3,6)$
From the above diagram it's clear. Is this problem wrongly written or am I missing something here?