# choosing possible routes home

• May 7th 2010, 07:09 PM
ihavvaquestion
choosing 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 PM
gmatt
subtle hint: what does every path that you can take have in common with all other such paths?
• May 7th 2010, 07:33 PM
ihavvaquestion
it goes north a certain amount and east a certain amount? it gets you home?
• May 7th 2010, 11:26 PM
gmatt
further hint: yes, take that reasoning further. Try to come up with a way to construct all walks.
• May 8th 2010, 04:03 AM
ihavvaquestion
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 PM
gmatt
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 PM
ihavvaquestion
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 PM
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.
• May 8th 2010, 02:56 PM
ihavvaquestion
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 PM
Plato
Quote:

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.
• May 8th 2010, 03:11 PM
gmatt
Quote:

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.
• May 8th 2010, 03:23 PM
ihavvaquestion
thanks...i was not sure how to go about posting in symbols...i will check it out...thanks to you both for your help