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Bunuel

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Re M04-14 [#permalink]

15 Sep 2014, 23:22

Kudos

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Expert Reply

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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samusa

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Joined: 01 Nov 2013

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Re: M04-14 [#permalink]

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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Bunuel

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Joined: 02 Sep 2009

Posts: 80298

Re: M04-14 [#permalink]

13 Jun 2015, 07:52

Expert Reply

samichange wrote:

Bunuel wrote:

Yes, you are correct.
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hessen923

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Joined: 08 Aug 2014

Posts: 7

Re: M04-14 [#permalink]

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!

Bunuel

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Posts: 80298

Re: M04-14 [#permalink]

15 Jul 2015, 00:03

Expert Reply

hessen923 wrote:

Have you read this part of the question: Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
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hessen923

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Re: M04-14 [#permalink]

15 Jul 2015, 08:57

I read that part but, to be honest, did not understand what it meant.

Bunuel

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Posts: 80298

Re: M04-14 [#permalink]

15 Jul 2015, 09:01

Expert Reply

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.
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CountClaud

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Re: M04-14 [#permalink]

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 re-worded 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...

Bunuel

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Posts: 80298

Re: M04-14 [#permalink]

20 Aug 2015, 07:43

Expert Reply

CountClaud wrote:

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.

Edited the question. Is it OK now?
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CountClaud

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M04-14 [#permalink]

30 Aug 2015, 07:46

Bunuel wrote:

CountClaud wrote:

Edited the question. Is it OK now?

Much clearer. Thanks, Bunuel!

dmaze01

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Posts: 8

Re: M04-14 [#permalink]

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.

wwambugu14

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Re: M04-14 [#permalink]

06 May 2017, 00:40

How is 7!/6! coming up??

kerin

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Re: M04-14 [#permalink]

15 Jun 2017, 04:39

Bunuel
If the question had been about unique Bs & Gs, then the answer should have been 7*5!*6!, correct?

Bunuel

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Joined: 02 Sep 2009

Posts: 80298

Re: M04-14 [#permalink]

15 Jun 2017, 05:38

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kerin wrote:

Bunuel
If the question had been about unique Bs & Gs, then the answer should have been 7*5!*6!, correct?

No, in this case the answer would be 7!*5!.

Glue b's together, we'll get 7 units:
{bbbbb}{g}{g}{g}{g}{g}{g}

# of arrangements = 7!. 5 g's within their unit can be arranged in 5! ways. So, 7!*5!.
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NickBrady

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Re: M04-14 [#permalink]

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?

SShawarma

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Joined: 06 Mar 2018

Posts: 2

Re M04-14 [#permalink]

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.

gurudabl

Manager

Joined: 09 Jun 2019

Posts: 91

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Re: M04-14 [#permalink]

01 Nov 2019, 01:18

Hi Bunuel Could help clear my small query?

If the word "identical" didn't exist in the question then would this be the answer (using the alternate method): 7! * 5! = answer ?

Thank You,
Dablu

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Re: M04-14 [#permalink]

15 Apr 2020, 16:32

Kudos

Bunuel wrote:

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

Keep in mind they are all identical. So G1G2 is same as G2G3. Well, every G is just G.

Now. We have 5Bs and 6Gs.

We need to keep Bs together. That means we can spread out the Gs

_ G _ G _ G _ G _ G _ G _

6 Gs will create 5 spaces between them and two at the corners. Now at any space you will have to put all the Bs and ignore all other Spaces.

There are only 7 ways in which you can do this.

Answer E
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