It is currently 13 Dec 2017, 20:45

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

CEO
Joined: 20 Nov 2005
Posts: 2892

Kudos [?]: 337 [1], given: 0

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

22 Jan 2006, 00:44
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

40% (02:16) correct 60% (00:54) wrong based on 25 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

Kudos [?]: 337 [1], given: 0

Director
Joined: 17 Dec 2005
Posts: 544

Kudos [?]: 40 [0], given: 0

Location: Germany

### Show Tags

22 Jan 2006, 05:11
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

Can't imagine that there are so many arrangements, will see what the others get.

Kudos [?]: 40 [0], given: 0

SVP
Joined: 14 Dec 2004
Posts: 1681

Kudos [?]: 172 [0], given: 0

### Show Tags

22 Jan 2006, 05:41
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

Kudos [?]: 172 [0], given: 0

VP
Joined: 29 Dec 2005
Posts: 1337

Kudos [?]: 70 [1], given: 0

### Show Tags

22 Jan 2006, 07:34
1
KUDOS
1
This post was
BOOKMARKED
b = 5
g = 6
total = 11
total seats = 12

no of ways boys can be seated = 5!
no of ways girls can be seated = 6!
we can only interperse boys in between girls since no girls and no boys can be adjacent.
since there are 12 fixed seats, so 5! 6! arrangements can be done = 12 ways.
so the no of total arrangements = 12 (6!) (5!)

Kudos [?]: 70 [1], given: 0

Manager
Joined: 15 Aug 2005
Posts: 132

Kudos [?]: 30 [0], given: 0

### Show Tags

22 Jan 2006, 15:59
1
This post was
BOOKMARKED
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

Kudos [?]: 30 [0], given: 0

Manager
Joined: 13 Aug 2005
Posts: 133

Kudos [?]: 1 [0], given: 0

### Show Tags

22 Jan 2006, 19:34

12*5!*6!

one empty seat - 12 ways of setting it up.
5 seats for 5 boys. - 5!
6 seats for 6 girls - 6!

Kudos [?]: 1 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 14854

Kudos [?]: 287 [0], given: 0

Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

18 Jun 2015, 18:48
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.
_________________

Kudos [?]: 287 [0], given: 0

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7793

Kudos [?]: 18119 [1], given: 236

Location: Pune, India
Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

18 Jun 2015, 19:50
1
KUDOS
Expert's post
8
This post was
BOOKMARKED
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
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18119 [1], given: 236

Math Expert
Joined: 02 Aug 2009
Posts: 5347

Kudos [?]: 6120 [1], given: 121

Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

18 Jun 2015, 20:44
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6120 [1], given: 121

SVP
Joined: 08 Jul 2010
Posts: 1857

Kudos [?]: 2400 [3], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

18 Jun 2015, 22:00
3
KUDOS
Expert's post
3
This post was
BOOKMARKED
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 [ 220.86 KiB | Viewed 9484 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

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

Kudos [?]: 2400 [3], given: 51

Math Expert
Joined: 02 Sep 2009
Posts: 42598

Kudos [?]: 135563 [0], given: 12699

Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

18 Jun 2015, 23:02
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.
_________________

Kudos [?]: 135563 [0], given: 12699

Intern
Joined: 01 Jun 2015
Posts: 10

Kudos [?]: 4 [0], given: 7

Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

01 Jul 2015, 10:08
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.

Kudos [?]: 4 [0], given: 7

Manager
Joined: 02 Jul 2015
Posts: 108

Kudos [?]: 35 [0], given: 58

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

14 Oct 2015, 04:47
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?

Kudos [?]: 35 [0], given: 58

SVP
Joined: 08 Jul 2010
Posts: 1857

Kudos [?]: 2400 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

14 Oct 2015, 05:33
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

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

Kudos [?]: 2400 [0], given: 51

Non-Human User
Joined: 09 Sep 2013
Posts: 14854

Kudos [?]: 287 [0], given: 0

Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

17 Jun 2017, 01:32
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.
_________________

Kudos [?]: 287 [0], given: 0

Manager
Joined: 02 Feb 2016
Posts: 90

Kudos [?]: 9 [0], given: 40

GMAT 1: 690 Q43 V41
Re: In how many ways 5 boys and 6 girls can be seated on 12 [#permalink]

### Show Tags

23 Sep 2017, 02:57
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?

Kudos [?]: 9 [0], given: 40

Intern
Joined: 25 Jul 2011
Posts: 44

Kudos [?]: 6 [1], given: 1058

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

23 Sep 2017, 03:30
1
KUDOS
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!
_________________

Kudos [?]: 6 [1], given: 1058

In how many ways 5 boys and 6 girls can be seated on 12   [#permalink] 23 Sep 2017, 03:30
Display posts from previous: Sort by