Robot in a grid problem

Question

In a 10*10 square grid,how many ways are there to move robot from (0,0) to (9,9). Robot can move 1 step left or 1 step up at a time.

Path from (4,4) to (5,4)  and path from (4,4) to (4,6) are broken,

Answer 1

Suppose we need to go from (0,0) to (3,3) then we need 3 right moves and 3 up moves in any order. 3 R's and 3 U's can be arranged in 6!/3!3! because total are 6 places choose 3 out of 6, put R's and in remaining 3 positions put U's. 6C3*3C3=6!/3!3!

Note- It is 18!/9!9! -(8!/4!4! * 8!/5!3!) in the below image: