Talk:2013 AMC 8 Problems/Problem 21

Could someone explain to me how to use combination to formulate the solution for the number of paths from Samantha's house to the SW point of the park and from the NW point to her school. What I don't understand is how do you come up with \binom42 respectively. What does 3 & 1 and 4 & 2 in the formula represent. I was able to enumerate the different paths, but could not figure out how to do it using the combinations formula.

TIA. Anay