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Tricia drives 8 miles from home to work. If she must follow

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Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 24 Jul 2007, 03:21
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31% (03:03) correct 69% (02:07) wrong based on 20 sessions
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Tricia drives 8 miles from home to work. If she must follow the roads shown in the square grid below, and each square has a side of one mile, then how many routes can Tricia follow from home to work?

A. 8
B. 12
C. 35
D. 45
E. 70



Home
--------
| | | | |
--------
| | | | |
--------
| | | | |
--------
| | | | |
-------- Work
[Reveal] Spoiler: OA
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Re: Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 24 Jul 2007, 04:14
This is actually a combinations question. She must walk up and to the right. There are four blocks up and four blocks to the right, so the answer is 8!/(4!4!)=70, E.
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Re: Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 24 Jul 2007, 06:20
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To get from home to work, she has to move up 4 times, and right 4 times.

So we can write a word UUUURRRR where U= up, R = right.

The number of ways to arrange this way is the number of routes she can take from home to work. So 8!/4!4! = 70
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Re: Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 25 Jul 2007, 09:18
hey guys
thanks for your responses
could you please explain how you applied the formula
i've always had trouble with combination questions

the answer is indeed correct
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Re: Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 25 Jul 2007, 13:41
So think about a person who has to walk this path:

Home
------
| | | |
------
| | | |
------Work

(Home to work) The person has to walk three blocks to the right and two blocks down. So the shortest way includes walking five blocks. There are 5!=120 ways to walk five blocks but there are two restrictions. One is that she has to walk two blocks down and the other is that she has to walk three blocks to the right. So there are only 5!/(3!2!)=10 ways to walk home. Does that make sense?
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Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 29 Sep 2014, 07:21
I am not convinced with that response. The question asks how many different routes are available for Tricia. Every right and down in that case should be unique, right?

The way I see it, if every turn (right or down) is a step, Tricia needs to take a total of 8 such steps to reach her destination. So at every step, she has 2 choices, either right, or down (South and East if you must). As such, the number of possible routes should be
2^8. Every route has to be unique. Can somebody please explain to me how my logic is incorrect?
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Re: Tricia drives 8 miles from home to work. If she must follow [#permalink] New post 29 Sep 2014, 07:30
Expert's post
nainaTan wrote:
I am not convinced with that response. The question asks how many different routes are available for Tricia. Every right and down in that case should be unique, right?

The way I see it, if every turn (right or down) is a step, Tricia needs to take a total of 8 such steps to reach her destination. So at every step, she has 2 choices, either right, or down (South and East if you must). As such, the number of possible routes should be
2^8. Every route has to be unique. Can somebody please explain to me how my logic is incorrect?


Does she have 2 choices on EVERY step? For example, if she's on upper right corner, how many choices does she have?
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Re: Tricia drives 8 miles from home to work. If she must follow   [#permalink] 29 Sep 2014, 07:30
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