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M16 #5, Pls answer

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Re: M16 #5, Pls answer [#permalink] New post 08 Aug 2012, 08:13
mikemcgarry wrote:
Yes, there are more advanced methods for keeping track of everything when it's far more than what anyone could visualize --- if you took an graduate-level course in Combinatorics, you could learn such things. But, again, that is leagues beyond what the GMAT expects.



Can you please hint on this? at least the topic of the graduate level course? I am curious.....thanks
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Re: M16 #5, Pls answer [#permalink] New post 12 Aug 2012, 08:01
for the first 5 blocks, there are 3x3x3x3x3=243 ways, and 3 out of 243 ways are when single color is used (RRRRR, WWWWW, BBBBB).

1. 240 ways : This is when each color has been used at least once but less than 5. So the 6th block can be any one of those three. So, 240x3=720.
2. 3 remaining ways : RRRRR+W, RRRRR+B, WWWWW+R, WWWWW+B, BBBBB+R, BBBBB+W, therefore 6.

720+6=726

Answer : E
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Re: M16 #5, Pls answer [#permalink] New post 09 Jun 2014, 20:27
Dear friends,

Though I have understood the logic of 3^6, I am unable to understand why we cannot apply the nPr formula in this problem (which gives wrong answer)

if there were 15 different colors then no of ways 6 tiles can be arranged will be 15P6

we have three colors repeating 5 times each

so the answer should be 15P6/ 5!*5!*5!

Can someone please help explain.
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Re: M16 #5, Pls answer [#permalink] New post 10 Jun 2014, 00:51
Expert's post
narendrjoshi wrote:
Dear friends,

Though I have understood the logic of 3^6, I am unable to understand why we cannot apply the nPr formula in this problem (which gives wrong answer)

if there were 15 different colors then no of ways 6 tiles can be arranged will be 15P6

we have three colors repeating 5 times each

so the answer should be 15P6/ 5!*5!*5!

Can someone please help explain.


15P6 gives the number of way to choose 6 items out of 15 different items so that the order of the selection is important.

15!/(5!5!5!) is the number of way to arrange 15 items out of which 5 are of one kind, 5 are of another kind, and the remaining 5 are also of another kind.

Dividing 15P6 by 5!5!5! doesn't make any sense.
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Re: M16 #5, Pls answer [#permalink] New post 10 Jun 2014, 03:00
Thanks a lot. I've understood my mistake.

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Re: M16 #5, Pls answer   [#permalink] 10 Jun 2014, 03:00
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