If home is represented by blue house and store is red, how many possible routes can we take to get from house to store?

Question

Map of our town is represented in the map below:

If home is represented by the blue house and the store is represented by a red store, how many possible routes can we take to get from our house to the store?

Answer 1

For ease of calculation we can mark 2 points 1 and 2 at the top right and bottom right vertices respectively of the cube adjacent to home.

Starting from 1 effectively we have to move 3 steps to the right and 4 steps to the down assuming a rectangular grid.
So for a rectangular grid the number of paths from 1 to store is
(3+4)C(3) = 7C3 = 35. But since 3 vertices are missing 5 possibilities are removed, leaving us with 30 ways from 1 to store

Starting from 2 we have (3+3)C(3) = 6C3 = 20 ways for a rectangular grid. Since 3 vertices are missing again 5 possibilities are removed, leaving us with 15 ways from 2 to store.

Adding the 2 we get 30 + 15 = 45 ways to reach the store from house.