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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]

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13 Jun 2012, 03:46
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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. $$2^53^2$$
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Re: As per the given figure, there are many horizontal and [#permalink]

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13 Jun 2012, 04:47
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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 $$\frac{9!}{5!4!}=\frac{9!}{5!*2*3*4}=\frac{9!}{6!*2^2}$$.

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]

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15 Oct 2014, 15:10
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Re: As per the given figure, there are many horizontal and   [#permalink] 15 Oct 2014, 15:10
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