1. choosing possible routes home

I have attached a question from my homework, that I am not sure how to get started.

2. subtle hint: what does every path that you can take have in common with all other such paths?

3. it goes north a certain amount and east a certain amount? it gets you home?

4. further hint: yes, take that reasoning further. Try to come up with a way to construct all walks.

5. every walk goes north 4 east 6
E6 N4
N4 E6

N3 E5 N1 E1
N3 E4 N1 E2
N3 E3 N1 E3
N3 E2 N1 E4
N3 E1 N1 E5

N2 E5 N2 E1
N2 E5 N1 E1 N1
N2 E4 N2 E2
N2 E4 N1 E2 N1
N2 E4 N1 E1 N1 E1
N2 E3 N2 E3
N2 E3 N1 E3 N1
N2 E3 N1 E2 N1 E1
N2 E3 N1 E1 N1 E2

N1 E6 N3
N1 E5 N3 E1
N1 E5 N2 E1 N1
N1 E5 N1 E1 N2
N1 E4 N3 E2
N1 E4 N2 E2 N1
N1 E4 N1 E2 N2
N1 E3 N3 E3
N1 E3 N2 E3 N1
N1 E3 N2 E2 N1 E1
N1 E3 N2 E1 N1 E2
N1 E3 N1 E3 N2
N1 E3 N1 E2 N2 E1
N1 E3 N1 E1 N1 E1 N1
N1 E2 N3 E4
N1 E2 N2 E4 N1
N1 E2 N1 E4 N3
N1

I see that I could trace every possible route, but how can i apply the fundemental counting principle to this problem?
it seems like this might be an nCr problem, but I cannot figure that out. can anyone help???

6. very strong hint:
Each walk goes 4 north 6 east as you observed. In total there are 10 steps (counting north or east.) Of these steps clearly 4 have to be north. What happens to the rest of the steps? How many ways are there to construct a path?

7. I appreciate your helping me, but I still don't get it. four steps must be north and six steps must be east???

is this an nCr problem? or is my thinking not right?

8. Let me be frank with you. I usually do not open attachments.
I just figure that someone who wants help should be willing to learn to post correctly.
But in the case, given the responses you have gotten, I will step in.
How many ways to rearrange the string $\displaystyle EEEEEENNNN?$
Any rearrangement of that string describes a way to drive from home to school.
Notice, that is the number of ways to place six E’s into ten places.

9. thanks frank, im ray! i am definitely willing to learn how to post correctly, but how do i go about doing that? how do i get a problem like this one typed into the message box?

so there would be 10C6 or 10C4 possible routes home then, correct?

10. Originally Posted by ihavvaquestion
so there would be 10C6 or 10C4 possible routes home then, correct?
That is correct.
Why not learn to post in symbols? You can use LaTeX tags.

11. Originally Posted by Plato
Let me be frank with you. I usually do not open attachments.
I just figure that someone who wants help should be willing to learn to post correctly.
But in the case, given the responses you have gotten, I will step in.
How many ways to rearrange the string $\displaystyle EEEEEENNNN?$
Any rearrangement of that string describes a way to drive from home to school.
Notice, that is the number of ways to place six E’s into ten places.
Sorry if I was being too round about, I'm not sure what level of guidance I should offer in such a case. Next time I can just give a straightforward reply like yours.

12. thanks...i was not sure how to go about posting in symbols...i will check it out...thanks to you both for your help