6. Consider the twodimensional Cartesian (standard rectangular m,'y) coordinate system on the plane. You move around the points with integer coordinates in such a way that, at each step you can go either one unit up or one unit to the right (that is, from (0, 0) you can go to either (1,0) or (0,1); from (2, 3) you can go either to (3,3) or (2,4), etc.) Count the number of different paths from the point (0,0) to (a) the point (4,3); (b) the point (4, 3), if you have to Visit the point (2, 2); (c) the point (4, 4), if you are not allowed to go above the line a; : 3; (but you are allowed to hit the line, e.g. by Visiting point the (1, 1))