Using Discrete math:
(a) How many lattice paths are there from (2,2) to (8,4)?
(b) How many lattice paths are there from (8,4) to (12,12)?
(c) How many lattice paths from (2,2) to (12,12) pass through (8,4)?
(d) How many lattice paths from (2,2) to (12,12) avoid (11,5)?