[tex] \Large \mathcal{SOLUTION:} [/tex]
[tex] \begin{array}{l} \textsf{Based on the given street map, Pascal's house} \\ \textsf{at P is 5 units east and 4 units south from the} \\ \textsf{Airport at A.} \\ \\ \textsf{In order to find the number of possible routes} \\ \textsf{from A to P, we must think of it as a set of} \\ \textsf{letters.} \\ \\ \textsf{Let:} \\ \quad \bullet \:\bold{E}\textsf{ be the 1 unit displacement to east from} \\ \quad \:\:\: \textsf{the taxi's current position;} \\ \quad \bullet \: \bold{S}\textsf{ be the 1 unit displacement to south from} \\ \quad \:\:\:\textsf{the taxi's current position.} \\ \\ \textsf{So P is 5 }\bold{E}\textsf{'s and 4 }\bold{S}\textsf{'s from A.} \\ \\ \textsf{Now the question is, in how many ways can we} \\ \textsf{arrange 5 }\bold{E}\textsf{'s and 4 }\bold{S}\textsf{'s in a string of 9 letters?} \\ \\ \textsf{By Distinguishable Permutation,} \\ \\ \dfrac{9!}{5! \: 4!} = \dfrac{9\times 8\times 7\times 6\times \cancel{5!}}{\cancel{5!} \times 4!} = \dfrac{3024}{24} = \boxed{126} \\ \\ \textsf{Thus, there are 126 possible routes from A to P.} \end{array} [/tex]
