Shortest Path Possible Corridors Question You find yourself in a maze, as shown below, and want to escape by the shortest route possible. The lines represent corridors, and you may only travel along corridors. How many different paths can you take? Note that both exits are 21 segments from the start point, so you should only count paths of length 21.


I do not want to know what the answer to this is... just an outline for a strategy. I was thinking about breaking this part up into each square and using permuations... is this logical?
Hint: There are $a+b\choose a$ ways to cross an $a\times b$ rectangle as in the problem statement.
Divide it into cases

Total Ways=number of ways to go to Exit $1$ $+$ number of ways to go to Exit $2$