This was from Greg’s video on Permutations. The solution is 7!/4!3!
For this, I thought it was going to be 24!/12!12! Because you have 12 “Norths” and 12 “Easts” so 24 letters total and then divided by the 12 North and 12 East.
It looks like you’re trying to partially count the edges, but I don’t see the logic behind that.
Consider a typical path (as outlined in the image): North → North → North → North → East → East → East
Since there are no “blockades” along our path, a different permutation is still valid because it contains the four “Norths” and three “Easts” required to reach our final destination.