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

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- May 7th 2010, 07:09 PMihavvaquestionchoosing possible routes home
I have attached a question from my homework, that I am not sure how to get started.

- May 7th 2010, 07:22 PMgmatt
subtle hint: what does every path that you can take have in common with all other such paths?

- May 7th 2010, 07:33 PMihavvaquestion
it goes north a certain amount and east a certain amount? it gets you home?

- May 7th 2010, 11:26 PMgmatt
further hint: yes, take that reasoning further. Try to come up with a way to construct all walks.

- May 8th 2010, 04:03 AMihavvaquestion
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??? - May 8th 2010, 01:47 PMgmatt
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? - May 8th 2010, 01:54 PMihavvaquestion
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? - May 8th 2010, 02:45 PMPlato
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. - May 8th 2010, 02:56 PMihavvaquestion
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? - May 8th 2010, 03:07 PMPlato
That is correct.

Why not learn to post in symbols? You can use LaTeX tags. - May 8th 2010, 03:11 PMgmatt
- May 8th 2010, 03:23 PMihavvaquestion
thanks...i was not sure how to go about posting in symbols...i will check it out...thanks to you both for your help