GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Oct 2018, 20:12

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.

Close

Request Expert Reply

Confirm Cancel

In how many ways 5 boys and 6 girls can be seated on 12

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

CEO
CEO
avatar
Joined: 20 Nov 2005
Posts: 2802
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 22 Jan 2006, 01:44
1
9
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (01:56) correct 50% (00:54) wrong based on 30 sessions

HideShow timer Statistics

In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8406
Location: Pune, India
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 18 Jun 2015, 20:50
2
7
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.


There are total 11 people and 12 chairs. Assume that V sits on the vacant chair. Now we have 12 chairs around a round table and 12 distinct "people".

Let's make the girls sit first.
One girl sits on any chair in 1 way (chairs around a table are not distinct relative to each other).
Now there are 11 distinct chairs (first to the girl's left, second to the girl's left, first to the girl's right etc).
Only 5 are available for the 5 girls - the chairs on either side of the girl are not available for girls. The girls can sit on only the alternate chairs. So 5 girls can sit on 5 distinct chairs in 5! ways.

Now 6 distinct chairs are leftover and 6 distinct people have to occupy them. This can be done in 6! ways.

Total number of arrangements = 1*5!*6! = 5! * 6!

Here are some posts on circular arrangements:

http://www.veritasprep.com/blog/2011/10 ... angements/
http://www.veritasprep.com/blog/2011/10 ... ts-part-i/
http://www.veritasprep.com/blog/2011/11 ... nstraints-–-part-ii/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

General Discussion
Director
Director
avatar
Joined: 17 Dec 2005
Posts: 533
Location: Germany
  [#permalink]

Show Tags

New post 22 Jan 2006, 06:11
I think the questions says that
1) the arrangements of boys and girls
2) the seats on which they sit are different and have to be counted too( Although it actually doesn't make much difference, because the table is round)

x=boys
_=girls
0=free space

_x_x_x_x_x_0


We see that the free space cannot be betwen a girl and a boy, because otherwise a girl would sit next to another girl.

Fix the free seat, then

1) there are 6!*5!=86400 arrangements

adjust for 2) 6!*5!*12=1036800

Can't imagine that there are so many arrangements, will see what the others get.
SVP
SVP
avatar
Joined: 14 Dec 2004
Posts: 1603
  [#permalink]

Show Tags

New post 22 Jan 2006, 06:41
Looks like new GMAT format with Quant section of 3 hours ;)

6G & 5B

1) No. of ways 6 girls can sit on 12 chairs = 12P6
2) No. of ways in which any 2 girls sit together = 12P5

There are 6 chairs left,
3) No. of ways 5 boys can sit on 6 chairs = 6P5

So, total = (12P6 - 12P5) * 6P5 :shock:
Manager
Manager
avatar
Joined: 15 Aug 2005
Posts: 129
Re: PS - Seating  [#permalink]

Show Tags

New post 22 Jan 2006, 16:59
1
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.


I come up with 6*5!*5!

No. of ways the girls can be seated on the round table with one vacant seat betwn all is (6-1)! = 5!
Now we have 6 vacant seats betn the girls-
select 5 seats out of 6 and arrange the boys=
5C6* 5!

so the no. of ways = 5!5!*6
Manager
Manager
avatar
Joined: 13 Aug 2005
Posts: 129
  [#permalink]

Show Tags

New post 22 Jan 2006, 20:34
I agree with allabout.

12*5!*6!

one empty seat - 12 ways of setting it up.
5 seats for 5 boys. - 5!
6 seats for 6 girls - 6!
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6980
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 18 Jun 2015, 21:44
1
1
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.


hi,
most of us have gone wrong in the solution by multiplying the answer by 12..
as pointed by Karishma, the answer should be 6!5!..
reasons:
the 12 seats can be equally divided in 6 seats each ..
here 6 seats(alternate) are occupied by 6 boys. so these can be placed in 6! but since it is a circular table, the ways are (6-1)!=5!
and remaining 6 can be arranged in following ways... choosing 5 out of 6 =6 ways and arranging these 5 seats in 5! ways.. so total =6*5!=6!
total ways 6!5!..

the question is same as arranging 6 boys and 6 girls in 12 seats across a circular table... only that the vacant seat can be taken as a girl's seat..
However the solution changes say if we have two vacant seats or the number of boys is not half of total seats..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

CEO
CEO
User avatar
P
Joined: 08 Jul 2010
Posts: 2569
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 18 Jun 2015, 23:00
4
3
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.



I will start solving this question from the Primary basic of Circular Arrangement (permutation).

In Circular Arrangement of Object we always fix one of the elements so that the repetition of arrangements (due to simultaneous movement of all objects in one of the directions) can be excluded

Here we Have 5 Boys, 6 Girls and 12 Chairs (Chairs Numbered from 1 to 12)

So Understand that one of the chairs will remain Vacant, Let's Fix the vacant chair only can call it CHAIR NO.1

Now, 6 Girls can sit only on chair no.s 2, 4, 6, 8, 10 and 12 only in 6! ways

And, 5 Girls can sit only on chair no.s 3, 5, 7, 9 and 11 only in 5! ways


i.e. Total ways of arranging all 11 people on 12 chairs with one chair vacant such that no boys sit together and no girls sit together = 5! * 6!
Attachments

File comment: www.GMATinsight.com
sol.jpg
sol.jpg [ 220.86 KiB | Viewed 12617 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 19 Jun 2015, 00:02
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.


Check other Arrangements in a Row and around a Table questions in our Special Questions Directory.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 01 Jun 2015
Posts: 10
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 01 Jul 2015, 11:08
It is a circular arrangement, so the order will not change if it is shifted.
We have a condition that no boy can sit by a girl, so the only arrangement can be

G B G B G B G B G B G _

B=5, so there are 5! ways to seat the boys
G=6, so there are 6! ways to seat the girls

Therefore there are 5!6! seating possibilities.
Manager
Manager
avatar
Joined: 02 Jul 2015
Posts: 106
Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 14 Oct 2015, 05:47
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.



Shouldn't the answer be calculated as 5!*6C5*5!

[ girls can sit in (6-1)! ways creating 6 spaces in which 5 boys have to sit so 6C5 and finally 5! ways to arrange those boys]

I know the answer is the same but is the approach right?
CEO
CEO
User avatar
P
Joined: 08 Jul 2010
Posts: 2569
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 14 Oct 2015, 06:33
longfellow wrote:
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.



Shouldn't the answer be calculated as 5!*6C5*5!

[ girls can sit in (6-1)! ways creating 6 spaces in which 5 boys have to sit so 6C5 and finally 5! ways to arrange those boys]

I know the answer is the same but is the approach right?


Yes your approach is absolutely correct given that fact that you have considered that girls will sit on 6 alternate chairs in (6-1)! ways in order to leave space of exactly 1 chair between any two adjacent Girls.
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
avatar
B
Joined: 02 Feb 2016
Posts: 89
GMAT 1: 690 Q43 V41
Re: In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 23 Sep 2017, 03:57
VeritasPrepKarishma wrote:
ps_dahiya wrote:
In how many ways 5 boys and 6 girls can be seated on 12 fixed chairs around a fixed circular table, so that no boy is seated adjacent to other boy and no girl is seated adjacent to other girl.


There are total 11 people and 12 chairs. Assume that V sits on the vacant chair. Now we have 12 chairs around a round table and 12 distinct "people".

Let's make the girls sit first.
One girl sits on any chair in 1 way (chairs around a table are not distinct relative to each other).
Now there are 11 distinct chairs (first to the girl's left, second to the girl's left, first to the girl's right etc).
Only 5 are available for the 5 girls - the chairs on either side of the girl are not available for girls. The girls can sit on only the alternate chairs. So 5 girls can sit on 5 distinct chairs in 5! ways.

Now 6 distinct chairs are leftover and 6 distinct people have to occupy them. This can be done in 6! ways.

Total number of arrangements = 1*5!*6! = 5! * 6!

Here are some posts on circular arrangements:

http://www.veritasprep.com/blog/2011/10 ... angements/
http://www.veritasprep.com/blog/2011/10 ... ts-part-i/
http://www.veritasprep.com/blog/2011/11 ... nstraints-–-part-ii/


Why does the solution become confusing all of a sudden if I place the boys first? It leaves 6 places for 6 girls and if we fix boys, as we placed them firstly, it gives (5-1)! = 4! for boys. Can you please help me get clear on this?
Manager
Manager
User avatar
S
Joined: 25 Jul 2011
Posts: 56
Location: India
Concentration: Strategy, Operations
GMAT 1: 740 Q49 V41
GPA: 3.5
WE: Engineering (Energy and Utilities)
In how many ways 5 boys and 6 girls can be seated on 12  [#permalink]

Show Tags

New post 23 Sep 2017, 04:30
1
Quote:
Why does the solution become confusing all of a sudden if I place the boys first? It leaves 6 places for 6 girls and if we fix boys, as we placed them firstly, it gives (5-1)! = 4! for boys. Can you please help me get clear on this?


TheMastermind
May be i could help..


You see....the condition given in the question stem says that "no boy is seated adjacent to other boy and no girl is seated adjacent to other girl"...
So if you place the boys first then you have got only 5 places in a fixed circular table to accommodate 6 girls (You can not use the 12th chair as it has to remain vacant )...thus forcing at least 2 girls to sit together...and violating the condition in the stem.....so...in circular combinations.. it becomes a thumb rule when such a condition is given in the stem ... arrange the type with higher number first and then arrange other types around them ....


for arranging 6 girls on a fixed circular table...total no. of ways =(n-1)!=5!
Now ...you have got 6 places on a fixed circular table to accommodate 5 Boys.
So.. accommodating 5 boys in 6 available places...total no. of ways =6*5*4*3*2=6!
So.....total no. of ways=5!*6!
_________________

Please hit kudos button below if you found my post helpful..TIA

GMAT Club Bot
In how many ways 5 boys and 6 girls can be seated on 12 &nbs [#permalink] 23 Sep 2017, 04:30
Display posts from previous: Sort by

In how many ways 5 boys and 6 girls can be seated on 12

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.