Q. How many paths are there when you move from (0,0) to (n,n) in the 1st quadrant of the graph, provided the constraint that you can move either one step above or one step right at any point of time.
Is the ans (2n)!/n!n! ?
This is Pascal's triangle. you should find that the number of ways of getting to, say the point with coordinates (6,0) is 1, the nbr of ways of getting to (5,1) is 6, the nbr to get to (4,2) is 6C2, and so on. So the nbr of ways of getting to (3,3) is 6C3 which is 6!/3!3!.