GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Apr 2020, 01:34

### 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

# In how many different ways can 3 boys and 3 girls be seated in a row

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Jan 2015
Posts: 25
In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

### Show Tags

30 Mar 2015, 10:35
1
8
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:15) correct 37% (01:21) wrong based on 164 sessions

### HideShow timer Statistics

In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96
Manager
Joined: 13 Apr 2016
Posts: 53
Location: India
GMAT 1: 640 Q50 V27
GPA: 3
WE: Operations (Hospitality and Tourism)
Re: In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

### Show Tags

07 May 2016, 07:51
5
Awli wrote:
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96

ans C
Figure attached
Attachments

1.jpg [ 304.35 KiB | Viewed 10759 times ]

##### General Discussion
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16361
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

### Show Tags

30 Mar 2015, 11:59
1
1
Hi Awli,

The prompt gives us the specific restriction that a boy can't sit next to another boy and a girl can't sit next to another girl. Since there are chairs on one side of the table and stools on the other side of the table, we have to account for 2 possible seating arrangements:

BGB
GBG

and

GBG
BGB

From here, we can use a simple permutation to get to the answer:

Moving from left-to-right....
For the first "spot", there are 3 different boys to choose from
For the second "spot", there are 3 different girls to choose from
For the third "spot", there then 2 different boys to choose from
For the fourth "spot", there are then 2 different girls to choose form
For the fifth and sixth "spots", we have the 1 boy and 1 girl that are left

(3)(3)(2)(2)(1)(1) = 36 possible seating arrangements for each of the two options.

(36)(2) = 72

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10244
Location: Pune, India
Re: In how many different ways can 3 girls and 3 boys be seated at a recta  [#permalink]

### Show Tags

30 Mar 2015, 23:21
1
Awli wrote:
In how many different ways can 3 girls and 3 boys be seated at a rectangular table that has 3 chairs on one side and 3 stools on the other side, if two girls or two boys can never sit side by side?

A. 24
B. 36
C. 72
D. 84
E. 96

Since 3 people will be on each side, and no two boys/two girls can sit together, on one side you will have Boy-Girl-Boy arrangement and on the other side you will have Girl-Boy-Girl arrangement.
From the 3 boys, choose 2 in 3C2 ways and a girl in 3C1 ways. Now you have split the boys and girls into BGB and GBG.
For BGB, pick a side (either chairs or stools) in 2 ways.
The girl takes the center seat and the 2 boys can be arranged around the girl in 2! ways.
On the other side, the boy sits in the center and the girls are arranged on his two sides in 2! ways.

Total arrangements = 3C2 * 3C1 * 2 * 2! * 2! = 72 ways.

_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager
Joined: 13 Oct 2016
Posts: 352
GPA: 3.98
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

04 Jan 2017, 00:12
1
3!*3!*2! = 6*6*2 = 72

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3447
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE: Education (Education)
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

04 Jan 2017, 01:32
3
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

Lets consider the group of all boys as one entity and group of girls as other entity

Now we have two entities to arrange which is possible in 2! ways

The group of boys within itself can be rearranged in 3! ways and
The group of Girls within itself can be rearranged in 3! ways

Total arrangements = 2!*3!*3! = 2*6*6 = 72

_________________
Prosper!!!
GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha)
e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi

My Recent Posts Q-1-Integer-Divisibility l Q-2-Inequality DS l Q-3-Standard Deviation l Q-4-Functions
ACCESS FREE GMAT TESTS HERE:22 FREE (FULL LENGTH) GMAT CATs LINK COLLECTION
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10244
Location: Pune, India
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

04 Jan 2017, 05:22
2
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

Bunch up the boys together and the girls together. Now we have to arrange 2 groups which we can do in 2! ways.

The boys within themselves can be arranged in 3! ways and the girls within themselves can be arranged in 3! ways.

Total arrangements = 2 * 3! * 3! = 72

For more on arrangements with constraints, check:
https://www.veritasprep.com/blog/2011/1 ... ts-part-i/
https://www.veritasprep.com/blog/2011/1 ... s-part-ii/
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 24 Jun 2016
Posts: 30
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

04 Jan 2017, 20:45
Condition: girls not separated..and boys are not separated

Count them as 1&1. Now we have 1boys n 1girl..

Arrangements =2!
And arrangements inside 3 girls & inside 3boys is=3! & 3!

Total=2!*3!*3! = 72 option C

Sent from my MotoG3 using GMAT Club Forum mobile app
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9960
Location: United States (CA)
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

06 Jan 2017, 09:57
Bunuel wrote:
In how many different ways can 3 boys and 3 girls be seated in a row of 6 chairs such that the girls are not separated, and the boys are not separated?

A. 24
B. 36
C. 72
D. 144
E. 288

We need to determine how many ways to arrange 3 boys and 3 girls in a row of six chairs when the boys must be seated together and the girls must be seated together. Since order matters, we have a permutation problem.

We can arrange the boys and girls as follows:

[B1)-B2)-B(3)] - [G(1)-G(2)-G(3)]

(Note: Since the boys must sit together and the girls must sit together, we have included the boys in one bracket and the girls in one bracket.)

Since we have 2 brackets, we can arrange those 2 brackets in 2! or 2 ways. However, we must account for the individual arrangements of the boys and the girls. The boys can be arranged in 3! or 6 ways and the girls can be arranged in 3! or 6 ways. Thus, the group can be arranged in 2 x 6 x 6 = 72 ways.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16361
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

26 Mar 2018, 12:34
1
Hi Al,

There are a number of ways to do the "math in this question", but here's a way that you might find easy:

The fact that we have 6 chairs in a row means that we'll likely be doing a permutation. We're given the specific rule that the seating will have to be either GGGBBB or BBBGGG.

The first chair can have either a boy or a girl:

6 _ _ _ _ _

Whether it's a boy or a girl, the next two chairs must be the same gender:

6 2 1 _ _ _

Then the next 3 chairs must be the other gender:

6 2 1 3 2 1

Now multiply:

6x2x1x3x2x1 = 72 possibilities.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Non-Human User
Joined: 09 Sep 2013
Posts: 14470
Re: In how many different ways can 3 boys and 3 girls be seated in a row  [#permalink]

### Show Tags

06 Oct 2019, 02:58
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: In how many different ways can 3 boys and 3 girls be seated in a row   [#permalink] 06 Oct 2019, 02:58
Display posts from previous: Sort by