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## Homework Statement

A taxi company is trying to find the quickest route during rush hour traffic from the train station to the football stadium. How many different routes must be considered if at each intersection the taxi must always move closer to the football stadium?

http://img179.imageshack.us/img179/4730/pathwayjh2.png [Broken]

[/URL]## Homework Equations

[tex]n_{P}_r=\frac{n!}{(n-r)!}[/tex]

## The Attempt at a Solution

My teacher told us that he didn't know how to solve this problem using permutations, and therefore solved it using pascal's triangle. This is what he did:

http://img81.imageshack.us/img81/162/pathway2oh6.png [Broken]

[/URL]As you see, he got the answer of 119, which is correct. However, I was wondering, is there a way of doing this question using the permutations equation? If not, is there another way of approaching this problem?

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