Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Aug 2015, 07:35
GMAT Club Tests

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Director
Director
avatar
Joined: 22 Aug 2007
Posts: 569
Followers: 1

Kudos [?]: 19 [0], given: 0

If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 10 Oct 2007, 22:36
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:52) correct 29% (01:37) wrong based on 112 sessions
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
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jun 2015, 01:38, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Manager
User avatar
Joined: 07 Sep 2007
Posts: 121
Followers: 2

Kudos [?]: 13 [0], given: 0

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 10 Oct 2007, 23:20
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 [_])
Senior Manager
Senior Manager
avatar
Joined: 27 Jul 2006
Posts: 298
Followers: 1

Kudos [?]: 8 [0], given: 0

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 11 Oct 2007, 03:16
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
Manager
Manager
avatar
Joined: 03 Oct 2007
Posts: 61
Followers: 4

Kudos [?]: 15 [0], given: 0

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 11 Oct 2007, 07:29
Not very well worded, but 7 seems right:

0B6
1B5
2B4
3B3
4B2
5B1
6B0
1 KUDOS received
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 421 [1] , given: 4

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 09 Jan 2008, 09:19
1
This post received
KUDOS
11 - 6 +1 = 7 elements to arrange

since the elements are uniform, we need to account for 6! repeats.

7!/6! = 7
_________________

You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

SVP
SVP
avatar
Joined: 28 Dec 2005
Posts: 1576
Followers: 2

Kudos [?]: 97 [0], given: 2

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 09 Jan 2008, 17:35
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.
CEO
CEO
User avatar
Joined: 29 Mar 2007
Posts: 2585
Followers: 17

Kudos [?]: 259 [0], given: 0

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 09 Jan 2008, 18:57
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.
1 KUDOS received
Manager
Manager
avatar
Joined: 27 Oct 2008
Posts: 185
Followers: 1

Kudos [?]: 116 [1] , given: 3

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 28 Sep 2009, 10:28
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.

Ans is E
1 KUDOS received
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1356
Followers: 14

Kudos [?]: 177 [1] , given: 10

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 02 May 2011, 22:25
1
This post received
KUDOS
total = 6 girls + 1 (set of boys together)
permutation = 7!/ 6!(set of girls can be arranged in 6! ways)
7
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6135
Followers: 342

Kudos [?]: 70 [0], given: 0

Premium Member
Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 17 Jun 2015, 00:20
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29157
Followers: 4730

Kudos [?]: 49885 [0], given: 7510

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink] New post 17 Jun 2015, 01:39
Expert's post
IrinaOK wrote:
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.


Answer: E.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the   [#permalink] 17 Jun 2015, 01:39
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic In how many ways can be 6 boys and 6 girls sit around circular table Bunuel 1 22 Jan 2015, 06:52
9 In how many ways can 5 boys be allotted four different rooms such that alphonsa 2 14 Sep 2014, 06:47
6 Experts publish their posts in the topic In how many ways can 5 boys and 3 girls be seated on 8 voodoochild 5 24 Sep 2012, 12:02
5 Experts publish their posts in the topic The music class consists of 4 girls and 7 boys. How many way bmwhype2 9 16 Oct 2007, 10:50
8 Experts publish their posts in the topic In how many ways 5 boys and 6 girls can be seated on 12 ps_dahiya 11 22 Jan 2006, 00:44
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.