How many different “up/right” paths are there from A to B which does not pass the vertex marked with "dot"

Question

I am trying to solve part B. Here, I am trying to do number of total paths - ways to go through the shop. Which should yield the number of ways to get from A to B without going through the shop. However, I am really confused about how to calculate the number of ways going through the shop. Any pointers would greatly be appreciated.

Answer 1

If you know how to do part (a) for a general case with $n$ rows and $m$ columns, you can use that to solve (b).

1. Count the total number of ways to get from home to school.
2. Count the number of ways to go from home to the shop.
3. Count the number of ways to go from the shop to school.
4. Combine the previous two to get the total number of ways to go to the shop and then to school.
5. Subtract this last result from the first one.