4.How many paths of minimum length are there from A to b in the grid below?

Notice that if we consider a move downward to the right as "Southeast" = "SE" and a move upward to the right as "Northeast" = "NE," we have the following possible set of moves from A to B :

( SE,SE, SE, NE, SE, NE, NE, NE )

So...the total number of possible minimum paths is given by choosing any four of eight positions in the set for "SE" (or, alternatively, choosing any four of eight positions in the set for "NE" ) =

C(8, 4) = 70 possible minimum paths