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

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Senior Manager
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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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A
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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
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 [#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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 [#permalink] New post 24 Jul 2007, 06:20
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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 [#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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 [#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?
  [#permalink] 25 Jul 2007, 13:41
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