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Pat will walk from intersection X to intersection Y along a route that

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Pat will walk from intersection X to intersection Y along a route that [#permalink]

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Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?

A. 6
B. 8
C. 10
D. 14
E. 16

[Reveal] Spoiler:
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[Reveal] Spoiler: OA
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Pat will walk from intersection X to intersection Y along a route that [#permalink]

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New post 14 Nov 2010, 09:09
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Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?

A) 6
B) 8
C) 10
D) 14
E) 16


In order the length to be minimum Pat should only go UP and RIGHT: namely thrice UP and twice RIGHT.

So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/(3!2!) = 10.

Answer: C.

Similar questions:
http://gmatclub.com/forum/grockit-simil ... re#p770816
http://gmatclub.com/forum/casey-and-the ... te#p812794

Hope it's clear.
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Re: Pat will walk from intersection X to intersection Y along a route that [#permalink]

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New post 14 Nov 2010, 09:16
as usual...awesome solution!

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Re: Pat will walk from intersection X to intersection Y along a route that [#permalink]

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New post 14 Nov 2010, 13:38
Cool solution...

Thanks Bunuel. +1
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Re: Pat will walk from intersection X to intersection Y along a route that [#permalink]

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New post 04 Mar 2018, 09:38
Hi :) I don’t understand why we are applying the combination formula instead of the permutation formula. Since we are going thrice up and twice right, and since there are many different ways to go thrice up and twice right, I thought that the order matters, in which case we should apply the permutation formula, no? Can someone explain to me please? Thank you!


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Re: Pat will walk from intersection X to intersection Y along a route that [#permalink]

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New post 04 Mar 2018, 09:43
Rurugu wrote:
Hi :) I don’t understand why we are applying the combination formula instead of the permutation formula. Since we are going thrice up and twice right, and since there are many different ways to go thrice up and twice right, I thought that the order matters, in which case we should apply the permutation formula, no? Can someone explain to me please? Thank you!


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We ARE taking into account the number of ways UUURR ca=ould be arranged: So combination of UUURR: # of permutations of 5 letters out of which there are 3 identical U's and 2 identical R's is 5!/(3!2!) = 10.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Pat will walk from intersection X to intersection Y along a route that [#permalink]

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New post 04 Mar 2018, 10:21
gmatexam2009 wrote:
Image
Pat will walk from intersection X to intersection Y along a route that is confined to the square grid of four streets and three avenues shown in the map above. How many routes from X to Y can Pat take that have the minimum possible length?

A. 6
B. 8
C. 10
D. 14
E. 16

[Reveal] Spoiler:
Attachment:
Q.png

Attachment:
Untitled.png

No matter which path he takes, Pat must take 3 Ups and 2 Rights. It is the same as arranging a 5 lettered word, with 3 Us and 2Rs. Hence 5C3.

To generalise, if there are m rows and n columns, the number of paths would be (m+n)Cm or (m+n)Cn.
Re: Pat will walk from intersection X to intersection Y along a route that   [#permalink] 04 Mar 2018, 10:21
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