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# M16 #5, Pls answer

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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08 Aug 2012, 13:33
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voodoochild wrote:
Can you please hint on this? at least the topic of the graduate level course? I am curious.....thanks

Frankly, I have not taken graduate level combinatorics myself. My gut sense is that the majority of highly complicated problems would be solved via technology. Take, for example, the freakish problem you proposed --- 100 tiles, 8 colors, and let's say 20 tiles of each color. How many possible combinations? By paper and pencil methods, that could take a very long time. I think the shortest way for anyone to do this would be to write a program that enumerates possibilities, somehow counting only the ones that fit the constraints. I'm not really a programmer, but I believe this would be a not-very-hard thing to program.

As I said, all this is well out of the league of anything the GMAT would expect you to do. Notice, for example, in the original problem in this thread, we were given the saving grace that there were five of each color --- just one less than the number of tiles on the floor --- and that allowed for the extremely slick and elegant solution discussed above. The GMAT is absolutely not interested in posing problems that require nightmarish levels of analysis to solve. By contrast, they are all about problems that lend themselves beautifully to surpassingly elegant solutions. Most larger combinatorics problems do NOT fall in that category. That's why those question are irrelevant to GMAT preparedness.

Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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12 Aug 2012, 09:01
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

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09 Jun 2014, 21:27
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!

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10 Jun 2014, 01:51
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!

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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10 Jun 2014, 04:00
Thanks a lot. I've understood my mistake.

Posted from my mobile device

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Re: M16 #5, Pls answer   [#permalink] 10 Jun 2014, 04:00

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# M16 #5, Pls answer

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