Living in NY, I came across this situation.
From Point A, to Point B, if I want to go by walk, how many routes are possible?
Example: Grand Central to Port Authority.
Grand Central is on 43rd and Park Ave. Port Authority is on 8th Ave and 41 st Street.
There are five avenues between Park and 8th (Madison,5th,6th,7th and 8th).
Is there a formula to find out how many routes are feasible to walk between two points in NY?
On
To come up with an exact answer I need to do some simplifications. First of all, your map must be a completely rectangular grid (Manhattan above $14$th street is almost that, but Central Park, Broadway and others ruin the simplicity). Also, I assume you never want to go further away from your goal.
Bearing these in mind, you want to go $m$ blocks north/south, and $n$ blocks east/west, and it can be done in any order. Then the total number of ways to walk from $A$ to $B$ is $$ \binom{m+n}{m} = \binom{m+n}{n} $$ which in some books is written $_{m+n}C_m = {}_{m+n}C_n$.
If you can get from Grand Central to Port Authority in at least two ways such that these routs don't share any point along the way, then you simply add all the possible routs. Otherwise, multiply.