Find the number of paths from A to B (Each step can only go up or to the right.)
We have the following set of moves (in any order )
( R, R, R, R , U , U , U , U)
Choose any 4 of 8 positions to put the U's in or any 4 of 8 positions to put the R's in
The number of paths = C (8,4) = 70
