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

It is currently 22 Oct 2019, 00:06

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

Six boys and six girls sit in a row at random. Find the probability th

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58405
Six boys and six girls sit in a row at random. Find the probability th  [#permalink]

Show Tags

New post 28 Jan 2019, 05:47
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

50% (01:46) correct 50% (02:15) wrong based on 35 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5027
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: Six boys and six girls sit in a row at random. Find the probability th  [#permalink]

Show Tags

New post 28 Jan 2019, 06:46
Bunuel wrote:
Six boys and six girls sit in a row at random.Find the probability that the boys and girls sit alternately.


A. 1/66

B. 1/132

C. 1/231

D. 1/462

E. 1/623


If the boys and girls sit alternatively
The required probability in that case would be given by
= 2 * 6! * 6!/ 12!
= 1/462.
Senior Manager
Senior Manager
User avatar
P
Joined: 13 Jan 2018
Posts: 342
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
Re: Six boys and six girls sit in a row at random. Find the probability th  [#permalink]

Show Tags

New post Updated on: 29 Jan 2019, 01:25
Total no. of ways of arranging 12 people are 12! ways

(i) _B_B_B_B_B_B_

6 boys can be arranged in 6! ways. Now, these 6 girls can be arranged in 6! ways.

Total possible arrangements are \(6!*6!\)
There are such cases possible in this manner.

So total possible cases are \(2*6!*6!\)

Required probability is \(\frac{2*6!*6!}{12!}\)

\(\frac{2*2*3*4*5*6}{7*8*9*10*11*12}\)

\(\frac{3*4}{7*8*9*11}\)

\(\frac{1}{42*11}\)

\(\frac{1}{462}\)

OPTION: D
_________________
____________________________
Regards,

Chaitanya


+1 Kudos

if you like my explanation!!!

Originally posted by eswarchethu135 on 28 Jan 2019, 08:13.
Last edited by eswarchethu135 on 29 Jan 2019, 01:25, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 14 Nov 2016
Posts: 7
WE: Consulting (Consulting)
GMAT ToolKit User
Re: Six boys and six girls sit in a row at random. Find the probability th  [#permalink]

Show Tags

New post 28 Jan 2019, 08:55
Total 6 boys and 6 girls :12!
Boy and girl alternative: 6! *6! *2 ways
boy first 6! *6! or girl first 6! *6!.
= 2 . 6! . 6!/ 12!
= 1/462
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8125
Location: United States (CA)
Re: Six boys and six girls sit in a row at random. Find the probability th  [#permalink]

Show Tags

New post 30 Jan 2019, 19:12
Bunuel wrote:
Six boys and six girls sit in a row at random. Find the probability that the boys and girls sit alternately.


A. 1/66

B. 1/132

C. 1/231

D. 1/462

E. 1/623


We have the following two arrangements:

B - G - B - G - B - G - B - G - B - G - B - G

or

G - B - G - B - G - B - G - B - G - B - G - B

Each arrangement will yield the same result, so we have:

[(6 x 6 x 5 x 5 x 4 x 4 x 3 x 3 x 2 x 2 x 1 x 1) x 2. This is the number of ways that we can have alternating boys and girls in the seating arrangement.

We can simplify this as (6! x 6! x 2).

We now note that the TOTAL number of ways of seating the 12 children is 12!

Thus, the probability that the boys and girls sit alternately is:

(6! x 6! x 2)/12!

Simplifying, we have:

(6 x 5 x 4 x 3 x 2 x 2)/(12 x 11 x 10 x 9 x 8 x 7) =1/(11 x 3 x 2 x 7) = 1/462

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 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.

GMAT Club Bot
Re: Six boys and six girls sit in a row at random. Find the probability th   [#permalink] 30 Jan 2019, 19:12
Display posts from previous: Sort by

Six boys and six girls sit in a row at random. Find the probability th

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





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