Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

10 Oct 2007, 23:36

12

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

70% (01:59) correct
30% (01:51) wrong based on 356 sessions

HideShow timer Statistics

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.

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

11 Oct 2007, 00:20

IrinaOK wrote:

The 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? (assume all members of the group are uniform and combinations within the group do not matter).

A 120 B 30 C 24 D 11 E 7

E. 7 Since members are uniform.

Let [B] be a cluster of boys such that all 5 are next to eachother.

_G_G_G_G_G_G_

We see that there is exactly 7 places for [B] to go (marked as an underscore [_])

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

11 Oct 2007, 04:16

I have seen this question before, but it could be 7 true, but it could be higher if only the group of boys is to be counted as a group. If the girls can be rearranged then...it will be higher

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

09 Jan 2008, 18:35

Got 7 as well. I thought about it like this:

_ _ _ _ _ _ _ _ _ _ _

There's 11 spots to fill, and the five boys have to be together. Start from the left and take up the first 5 spots: thats one way. Then, move one spot to the right, and take up the next 5, thats two ways. Keep going until you run out of space and youll see there are only 5 ways.

One thing to note is that the stem said that a different arrangements dont matter. If it did, we'd have many more ways, since in each 'way', the boys can be arranged in 5! ways.

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

09 Jan 2008, 19:57

IrinaOK wrote:

The 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? (assume all members of the group are uniform and combinations within the group do not matter).

A 120 B 30 C 24 D 11 E 7

I couldnt figure out how to do this via combinatorics equations so I just wrote it down.

BBBBBGGGGGG. Had bout 30sec left and it dawned on me that all we have to realize is that we can arrange it

GBBBBBGGGGG, GGBBBBBGGGG etc... I count 7. U dont have to write all of these out just realize u can have 5 inbetween G's and 2 on the outside.

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

28 Sep 2009, 11:28

1

This post received KUDOS

The 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? (assume all members of the group are uniform and combinations within the group do not matter).

A 120 B 30 C 24 D 11 E 7

Soln. Since combinations within the group not matter, and since all boys go together. We can group all 5 boys into 1 group. The 6 girls and the 1 group of boys can be arranged in 7 ways.

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

17 Jun 2015, 01:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

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

M04-14

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.

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

02 Jul 2016, 21:25

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]

Show Tags

24 Sep 2016, 10:00

two boys (or two girls) are not different. see this question as the arrangement of 5 letters B and 6 letters G.

condition - letters B are together.

[BBBBB] G G G G G G --> so we have 7 elements (bracket as one element) here. arrangement for these 7 elements is 7! Now 6 out of these 7 elements are same i.e. G. in such case we divide by 6!

rule - in the arrangement of n elements if there are p,q,r .. are similar elements then arrangements are - n!/(p!*q!*r!...)

hence arrangement in above case is - 7!/6!

what about the elements in bracket? yes so arrangements for 5 B's are 5! BUT 5 elements are same so we divide by 5!. so essentially arrangements are = 5!/5!

Total Arrangements = (7!/6!) * (5!/5!) = 7 _________________

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...