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Pat will walk from intersection X to intersection Y along a

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Manager
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Pat will walk from intersection X to intersection Y along a [#permalink] New post 15 Jun 2006, 19:04
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Pat will walk from intersection X to intersection Y along a route that is confind to the square grid of four streets and three avenues. (If you draw a grid, you have 4 horizontal lines and 3 vertical lines. X is on your lower left and Y is on your upper right. This problem is #195 in OG11)

How many routes can Pat tale that have the min possible length?

a) 6

b) 8

c) 10

d) 14

e) 16

Does anyone have a logically method of solving this problem with simply writing out all the possiblity? What is the logically basis?

Thanks.

Mike
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 [#permalink] New post 15 Jun 2006, 19:39
Given that Pat has to take a total of 5 steps reach from X to Y, and at each steps the shortest route can be attained by either moving Right or Up, the total routes
= # of steps to be taken x # of choices @ each step
= 5 x 2 = 10 ??
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 [#permalink] New post 15 Jun 2006, 21:20
The shortest routes all involve walking to the right twice, and up thrice.

So you can write the word RRUUU where R stands for right, and U stands for up.

Now the number of routes is just the number of permutations, which is 5!/3!2! = 10 ways.
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 [#permalink] New post 15 Jun 2006, 21:43
10.

Three routes up and two routes to the right.

Total = 5!/3!2! = 10
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 [#permalink] New post 15 Jun 2006, 22:12
Please refer to this post :
http://www.gmatclub.com/phpbb/viewtopic.php?t=30301

Giddi does a great job in explaing the approach to route problems.
  [#permalink] 15 Jun 2006, 22:12
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