Permutations and combinations on a paths


#1

suppose that a robot is placed on the cartesian plane.At each step it is allowed to move either 1 unit up or 1 unti right,i.e.,if is at (i,j) then it can move to either(i+1,j) or (i,j+1).
suppose that the robot is not allowed to traverse the line segment from (4,4) to (5,4).with this constraint,how many distinct paths are there for the robot to reach (10,10) strting from (0,0)?


#2

#3

I Think answer is 20C10 - 10C5