Binomial Expansion Word Problem (Creating a Equation) I was working on my math textbook (Nelson Functions 11) and came across the following word problem. This question is shown in the "Pascal's Triangle and Binomial Expansions" section of the book.

"Using the diagram at the left (shown below), determine the number of different ways that Joan could walk to school from her house if she always travels either north or east."

(Please note that Joan walks on the black lines and not on the white squares)
Diagram:

I'm pretty sure that the question involves me simply finding a binomial expression in the form (a+b)^n and expanding it, as that was what we learned in class before this question was assigned. However, I have no idea how that or Pascal's Triangle could relate to this problem (looks more like probability to me) and I don't know how to find the equation used to solve this problem.
 A: HINT: Label each intersection with the number of ways in which Joan can reach it. She can reach her house in exactly one way: she takes no steps. She can reach the intersection a block to the east in one way: she must take one eastward step. Similarly, she can reach the intersection a block to the north in one way: she must take one northward step. She can reach the intersection one block to the northeast of her house, however, in two ways: she can go east, then north, or she can go north, then east.
I’ve started the labelling process in the grid below, whose cells correspond to the street intersections, not to the city blocks; I’ve included two more labels besides the ones mentioned above. Note that in general, she can reach each intersection either from the one immediately south of it or from the one immediately west of it, unless it’s on the southern or western boundary of the square.
$$\begin{array}{|c|c|c|c|c|} \hline
?&?&?&?&?&?\\ \hline
?&?&?&?&?&?\\ \hline
?&?&?&?&?&?\\ \hline
1&3&?&?&?&?\\ \hline
1&2&3&?&?&?\\ \hline
1&1&1&?&?&?\\ \hline
\end{array}$$
If you finish filling in the labels correctly, both the labels themselves and the way in which you calculated them should give you the connection with Pascal’s triangle.
A: Joan will walk a total of $10$ blocks. Of these, $5$ will be northward, and $5$ eastward. 
A path she takes is completely described by a "word" of length $10$, made up of $5$ occurrences of the letter N, and $5$ occurrences of the letter E. For example, NNENNNEEEE describes the walk that went north for $2$ blocks, then east for $1$ block, then north for $3$ blocks, and finally east for $4$ blocks.
Any word corresponds to a walk, any walk is described by a word. So there are just as many ways to get to school as there are words of length $10$ made up of $5$ N's and $5$ E's. 
How many such words are there? We must choose the $5$ positions in the word where the N's will go. There are $\binom{10}{5}$ ways to do this. The number may be called $C(10,5)$ in your book, or $C_5^{10}$, or ${}^{10}C_5$. It is the middle entry of the $10$th line in Pascal's Triangle (which was known in China centuries before Pascal).  
A: Joan could walk to school from her house $252$ different ways:
Since she always travel either north or east, that's $10$ occurrences.
Completing cells which corresponds to the street intersection leads to Pascal's triangle.The summation of all the cells excluding the cells that has number one (1) totals $242$ plus $10$ occurrences for north and east equals $252$.
You could also solve this by using binomial expansion: $(a + b)^n$
