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15 Sep 2014, 23:22
Official Solution:In how many ways 5 identical blue marbles and 6 identical green marbles can be arranged in a row, so that all the blue marbles are together?A. 120 B. 30 C. 24 D. 11 E. 7 There are 7 possibilities: bbbbbgggggg gbbbbbggggg ggbbbbbgggg gggbbbbbggg ggggbbbbbgg gggggbbbbbg ggggggbbbbb Formally, \(\frac{7!}{6!} = 7\). Alternative explanation: Think of all 5 blue marbles as a single unit. Together with 6 green marbles we'd have a total of 7 units. The difference between the arrangements is the position of the blue marbles (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the blue marbles which can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well. Answer: E
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Re: M0414
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12 Jun 2015, 10:20
Bunuel wrote: Official Solution:
If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
A. 120 B. 30 C. 24 D. 11 E. 7
There are 7 possibilities: bbbbbgggggg gbbbbbggggg ggbbbbbgggg gggbbbbbggg ggggbbbbbgg gggggbbbbbg ggggggbbbbb Formally, \(\frac{7!}{6!} = 7\). Alternative explanation: Think of all 5 boys as a single unit. Together with 6 girls it makes a total of 7 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well.
Answer: E Hi Bunnel What do we mean by the following statement Do not differentiate between arrangements that are obtained by swapping two boys or two girls. Do we mean to say that we need to ignore the {5!} and {6!} ways in which the boys and girls can be arranged among themselves....?? This is what I understood.Please clarify. Thanks
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13 Jun 2015, 07:52
samichange wrote: Bunuel wrote: Official Solution:
If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
A. 120 B. 30 C. 24 D. 11 E. 7
There are 7 possibilities: bbbbbgggggg gbbbbbggggg ggbbbbbgggg gggbbbbbggg ggggbbbbbgg gggggbbbbbg ggggggbbbbb Formally, \(\frac{7!}{6!} = 7\). Alternative explanation: Think of all 5 boys as a single unit. Together with 6 girls it makes a total of 7 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well.
Answer: E Hi Bunnel What do we mean by the following statement Do not differentiate between arrangements that are obtained by swapping two boys or two girls. Do we mean to say that we need to ignore the {5!} and {6!} ways in which the boys and girls can be arranged among themselves....??This is what I understood.Please clarify. Thanks Yes, you are correct.
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14 Jul 2015, 12:34
Bunuel
I don't understand. I've seen any number of questions of this type. They are invariably permutations questions. If a bunch of people are put in a row then every arrangement, whether Paul is to the left of Michael or Michael is to the left of Paul, is different from every other arrangement.
In this case, the answer should be 5! x 7!



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15 Jul 2015, 00:03



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15 Jul 2015, 08:57
I read that part but, to be honest, did not understand what it meant.



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05 Aug 2015, 03:40
Bunuel wrote: hessen923 wrote: I read that part but, to be honest, did not understand what it meant. It means that we are not interested in arrangements of girls and boys in their groups. I think that should be reworded in a clearer fashion. The fact that the problem mentioned two girls led me to look at permutation gbbbbbggggg as being able to rotate the first girl with any of the other remaining 5 girls. Apologies but the sentence " swapping two boys or two girls" does not make much sense to me...



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20 Aug 2015, 07:43



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Bunuel wrote: CountClaud wrote:
I think that should be reworded in a clearer fashion. The fact that the problem mentioned two girls led me to look at permutation gbbbbbggggg as being able to rotate the first girl with any of the other remaining 5 girls. Apologies but the sentence " swapping two boys or two girls" does not make much sense to me...
Edited the question. Is it OK now? Much clearer. Thanks, Bunuel!



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20 Jul 2016, 18:43
Should clarify to say "unique patterns." The problem attempts to do this by saying "identical" marbles. But this technically doesn't imply that marble 1,2,3,4,5,6,7 are interchangeable. I can move 2,1,3,4,5,6,7 and that seems like a different position to me, even if they are all the same size, weight, color etc. Unless, that's exactly what "identical" means on the GMAT, would be good to know if I am right or wrong. Logically, it doesn't seem like a strong enough implication per my example.



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06 May 2017, 00:40
How is 7!/6! coming up??



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15 Jun 2017, 04:39
BunuelIf the question had been about unique Bs & Gs, then the answer should have been 7*5!*6!, correct?



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15 Jun 2017, 05:38



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02 Oct 2018, 11:20
Question wording is wrong:
In how many ways 5 identical blue marbles and 6 identical green marbles can be arranged in a row, so that all the blue marbles are together?



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02 Oct 2018, 23:19
"Do not differentiate between arrangements that are obtained by swapping two boys or two girls" is missing in the question.










