find all pathbetween 2 node under constraint

hey

i want to find all path between A to B ( start from left buttom)

i have tryed to use meshgrid and allpath command without succses

the constraint are the i can go right or up only

also, i need to write code that calculates the probability on each node to go up or right if given that all route is equal probability

i will appreciate hint how to write my code and which commands to use

here is the mesh