How to solve this combinatorics problem? !enter image description here As a tourist in NY, I want to go from the Grand Central Station (42nd street and 4th Avenue) to Times Square (47th street and 7th Avenue). I needed my morning coffee, and wanted to go to a Starbucks that's located at 44th street and 5th avenue. If I only walk West and North, how many ways are there for me to get there?

I agree with Ofir's answer and would like to suggest an alternative, more general way to compute the number of ways to go from the cafe to Times square.

Clearly, the total number of steps is $5$. Clearly, exactly two of those steps are in the direction west. You just need to choose these two steps, and the number of possible choices is $$\left(\begin{array}{c}5\\\2\end{array}\right)=10.$$In general, if you need to go $n$ steps to the north and $k$ steps to the west, the number of possible ways for that will be$$\left(\begin{array}{c}n+k\\\k\end{array}\right)=\left(\begin{array}{c}n+k\\\
\end{array}\right)=\frac{(n+k)!}{n!k!}.$$