Author 
Message 
TAGS:

Hide Tags

Director
Joined: 22 Aug 2007
Posts: 566

If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
10 Oct 2007, 22:36
15
This post was BOOKMARKED
Question Stats:
76% (01:06) correct 24% (01:33) wrong based on 444 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. A. 120 B. 30 C. 24 D. 11 E. 7 M0414
Official Answer and Stats are available only to registered users. Register/ Login.
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
Joined: 07 Sep 2007
Posts: 115

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
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
Joined: 27 Jul 2006
Posts: 292

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
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
Joined: 03 Oct 2007
Posts: 60

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
11 Oct 2007, 07:29
Not very well worded, but 7 seems right:
0B6
1B5
2B4
3B3
4B2
5B1
6B0



CEO
Joined: 21 Jan 2007
Posts: 2734
Location: New York City

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
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
Joined: 28 Dec 2005
Posts: 1542

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
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
Joined: 29 Mar 2007
Posts: 2550

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



Manager
Joined: 27 Oct 2008
Posts: 183

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



VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1260

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
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.sustainablesphere.com/ Promote Green Business,Sustainable Living and Green Earth !!



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
17 Jun 2015, 01:39
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
M0414 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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? Extrahard Quant Tests with Brilliant Analytics



Moderator
Joined: 21 Jun 2014
Posts: 981
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
24 Sep 2016, 09:00
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
_________________
 Target  720740 http://gmatclub.com/forum/informationonnewgmatesrreportbeta221111.html http://gmatclub.com/forum/listofoneyearfulltimembaprograms222103.html



Intern
Joined: 16 Nov 2016
Posts: 31
Location: India
Concentration: Finance, International Business
GPA: 3.78
WE: Accounting (Accounting)

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
13 Jun 2017, 22:39
i have a problem understanding the question. why is the answer not 7!*5!



Intern
Joined: 14 Aug 2017
Posts: 33

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
26 Oct 2017, 00:06
Bunuel  I did figure out the question but i am still confused with the clause that has been mentioned in the stem :Do not differentiate between arrangements that are obtained by swapping two boys or two girls:Assuming this was would not had been provided in the stem would the answer still be 7? or would it jump to 7*5! (5! being the arrangement for the boys internally). Please help.



Intern
Joined: 07 Jul 2017
Posts: 10

Re: If a choir consists of 5 boys and 6 girls, in how many ways can the [#permalink]
Show Tags
28 Oct 2017, 06:41
Hello everyone,
struggling a bit on figuring out the right approach to solve problems based on combinations.
My first approach here was to calculate the number of possible arrangements considering the "anagram grid" formula, i.e. 11! / (5! x 6!)  which is clearly wrong, but I can't really grasp why. What would I be calculating in this way?
Thanks a lot for the support!




Re: If a choir consists of 5 boys and 6 girls, in how many ways can the
[#permalink]
28 Oct 2017, 06:41






