Find ways from $(0,0)$ to $(8,8)$ You are allowed only to go east or north. Because of road construction, you cannot touch the points $a, b, c$ and $d$. Under these restrictions, the number of ways that you can go from $(0, 0)$ and finish at $(8, 8)$ in the following figure is:

First, I used ${16\choose 8}$ to get the number of ways without this construction. I am a bit confused on what to do next...

Through $a$. $\binom{6}{3}\times\binom{10}{5}$.
Through $b$ without going through $a$. $\binom{6}{4}\times\binom{9}{4}$.
Through $d$ without going through $a$. $\binom{6}{2}\times\binom{9}{5}$.
$\binom{16}{8}-\binom{6}{3}\times\binom{10}{5}-\binom{6}{4}\times\binom{9}{4}-\binom{6}{2}\times\binom{9}{5}=4050$
