Find the number of pathways from A to B if you can only travel to the right and down. I would like to solve the following, using Pascal's Triangle. Since there are shapes withing shapes, I am unsure as to where I should place the values. 
EDIT 1:

Where do I go from here? How do I get the value for the next vertex?
EDIT 2:

Okay, how does this look? From this, I would have 22 pathways. 

Since we can go from $A$ to $B$ in at most eigth steps, we can compute the number of paths by computing the eigth power of the adjacency matrix of our configuration with a self-loop in $B$.
