5 girls and 3 boys are arranged randomly in a row : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 14:24

# Chicago-Booth

### 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

# 5 girls and 3 boys are arranged randomly in a row

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 25 Nov 2011
Posts: 261
Location: India
Concentration: Technology, General Management
GPA: 3.95
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 160 [0], given: 20

5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

19 Feb 2012, 05:08
11
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:54) correct 38% (02:06) wrong based on 210 sessions

### HideShow timer Statistics

5 girls and 3 boys are arranged randomly in a row. Find the probability that:

1) there is one boy on each end.
2) There is one girl on each end.

A. 3/28 & 5/14
B. 5/28 & 3/14
C. 5/14 & 3/28
D. 3/28 & 1/14
E. 1/28 & 5/14
[Reveal] Spoiler: OA

_________________

-------------------------
-Aravind Chembeti

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90025 [4] , given: 10402

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

19 Feb 2012, 05:25
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
Chembeti wrote:
5 girls and 3 boys are arranged randomly in a row. Find the probability that:

1) there is one boy on each end.
2) There is one girl on each end.

A. 3/28 & 5/14
B. 5/28 & 3/14
C. 5/14 & 3/28
D. 3/28 & 1/14
E. 1/28 & 5/14

Total # of arrangements is 8!;

1. The # of arrangements where there is one boy on each end is $$C^2_3*2*6!$$, where $$C^2_3$$ is # of ways to select which 2 boys will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;

$$P=\frac{C^2_3*2*6!}{8!}=\frac{3}{28}$$.

2. The # of arrangements where there is one girl on each end is $$C^2_5*2*7!$$, where $$C^2_5$$ is # of ways to select which 2 girls will be on that positions, *2 # of way to arrange them on that position (A------B and B------A) and 6! is # of arrangements of 6 people left;

$$P=\frac{C^2_5*2*6!}{8!}=\frac{5}{14}$$.

_________________
Intern
Joined: 07 Feb 2013
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 11

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

06 Mar 2013, 18:28
1
KUDOS
Hi Bunel, firstly I would like to thank you for all the help you've given to the forum! You have been nothing but superb!

I have a question on this though, would it be possible also to solve the question as below?
I had solved it like this initially and I'm not sure now if I have some mistakes in my fundamental theory.
It would be great if you could help clarify.
Thank you!

1)
[m]P=(P^2_3*6!)/8!

2)
[m]P=(P^2_5*6!)/8!
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90025 [1] , given: 10402

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

07 Mar 2013, 01:01
1
KUDOS
Expert's post
swyw wrote:
Hi Bunel, firstly I would like to thank you for all the help you've given to the forum! You have been nothing but superb!

I have a question on this though, would it be possible also to solve the question as below?
I had solved it like this initially and I'm not sure now if I have some mistakes in my fundamental theory.
It would be great if you could help clarify.
Thank you!

1)
[m]P=(P^2_3*6!)/8!

2)
[m]P=(P^2_5*6!)/8!

Yes, your approach is fine: 3P2=3C2*2! and 5P2=5C2*2!.

Hope it's clear.
_________________
Senior Manager
Joined: 23 Oct 2010
Posts: 386
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Followers: 21

Kudos [?]: 316 [1] , given: 73

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

09 Mar 2013, 02:17
1
KUDOS
1
This post was
BOOKMARKED
one boy on each end = (3/8)*(2/7)=3/28
one girl on each end =(5/8)*(4/7)=5/14
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Senior Manager
Joined: 02 Sep 2012
Posts: 259
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 5

Kudos [?]: 178 [0], given: 99

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

09 Mar 2013, 05:06
bunnel,
Any problem of similar type available in this forum??? if so can you please tag those ..thanks in advance
_________________

"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90025 [2] , given: 10402

5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

10 Mar 2013, 05:02
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12887
Followers: 561

Kudos [?]: 158 [0], given: 0

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

19 Jul 2014, 08:14
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12887
Followers: 561

Kudos [?]: 158 [0], given: 0

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

24 Aug 2015, 11:08
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12887
Followers: 561

Kudos [?]: 158 [0], given: 0

Re: 5 girls and 3 boys are arranged randomly in a row [#permalink]

### Show Tags

10 Sep 2016, 14:34
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: 5 girls and 3 boys are arranged randomly in a row   [#permalink] 10 Sep 2016, 14:34
Similar topics Replies Last post
Similar
Topics:
9 There are 6 girls and 6 boys. If they are to be seated in a row 5 29 Mar 2016, 03:49
22 In how many ways can 5 boys and 3 girls be seated on 8 17 24 Sep 2012, 12:02
5 In a certain school, the ratio of boys to girls is 5 to 13. 3 24 Sep 2012, 03:12
1 3 boys and 3 girls 9 19 Aug 2011, 22:59
70 The ratio of boys to girls in Class A is 3 to 4. The ratio 41 03 Apr 2010, 11:57
Display posts from previous: Sort by