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As per the given figure, there are many horizontal and

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As per the given figure, there are many horizontal and [#permalink] New post 13 Jun 2012, 02:46
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71% (01:55) correct 29% (01:39) wrong based on 14 sessions
As per the given figure, there are many horizontal and vertical roads connecting point A & B. What are the total number of shortest paths which can be used to travel from A to B without repeating any road?

A. 5!2!

B. \frac {9!}{2^26!}

C. \frac {9!}{6!}

D. 4!3!2!

E. 2^53^2
[Reveal] Spoiler: OA

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Re: As per the given figure, there are many horizontal and [#permalink] New post 13 Jun 2012, 03:47
Expert's post
cyberjadugar wrote:
As per the given figure, there are many horizontal and vertical roads connecting point A & B. What are the total number of shortest paths which can be used to travel from A to B without repeating any road?

A. 5!2!

B. \frac {9!}{2^26!}

C. \frac {9!}{6!}

D. 4!3!2!

E. 2^53^2


In order the length to be minimum one should only go RIGHT and DOWN: namely 5 times RIGHT and 4 times DOWN.

So combination of RRRRRDDDD: # of permutations of 9 letters out of which there are 5 identical R's and 2 identical D's is \frac{9!}{5!4!}=\frac{9!}{5!*2*3*4}=\frac{9!}{6!*2^2}.

Answer: B.

Proper versions of this question;
grockit-similar-to-og-quant-qustion-99962.html
casey-and-the-bus-104236.html
pat-will-walk-from-intersection-a-to-intersection-b-along-a-68374.html
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Re: As per the given figure, there are many horizontal and   [#permalink] 13 Jun 2012, 03:47
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As per the given figure, there are many horizontal and

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