NEW HERE? LEARN MORE
closeclose
Last visit was: 23 Apr 2024, 18:43 It is currently 23 Apr 2024, 18:43
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Four female friends & four male friends will be pictured in

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
Smita04
Manager
Manager
Joined: 29 Nov 2011
Posts: 66
Own Kudos [?]: 1256 [3]
Given Kudos: 37
Send PM
Four female friends & four male friends will be pictured in [#permalink] New post   Updated on: 05 Apr 2012, 03:59
3
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

59% (01:28) correct 41% (01:21) wrong based on 112 sessions
Hide Show timer Statistics
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?

A. 40320
B. 1680
C. 1152
D. 576
E. 70
ShowHide Answer
Official Answer
C

Originally posted by Smita04 on 05 Apr 2012, 01:30.
Last edited by Bunuel on 05 Apr 2012, 03:59, edited 1 time in total.
Edited the question and added the OA
User avatar
B
kraizada84
Manager
Manager
Joined: 13 Mar 2012
Posts: 155
Own Kudos [?]: 473 [0]
Given Kudos: 48
Concentration: Operations, Strategy
Send PM
Re: Probability [#permalink] New post   05 Apr 2012, 01:58
Smita04 wrote:
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row,with men & women alternating.How many possible arrangements may she chose?
A)40320
B)1680
C)1152
D)576
E)70


okay you got 2 ways of assigning alternate places to either male or female

hence 2

now any of the alternate 4 places can be filled by 4 male or female in 4!
similarily,
other 4 alternate places can be filled in 4!

hence required probability= 2*4!*4!=1152

hence C

Hope this helps..!!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618603 [1]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Four female friends & four male friends will be pictured in [#permalink] New post   05 Apr 2012, 04:03
1
Kudos
Expert Reply
Smita04 wrote:
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?

A. 40320
B. 1680
C. 1152
D. 576
E. 70


To meet the condition in the stem men and women should line up either: M-W-M-W-M-W-M-W or W-M-W-M-W-M-W-M. Now, for each of these two cases men can be arranged in 4! ways and women can be arranged also in 4! ways, hence total # of arrangements is 2*4!*4!=1,152.

Answer: C.

Hope it's clear.
User avatar
B
Anurag06
Intern
Intern
Joined: 10 Dec 2019
Posts: 42
Own Kudos [?]: 5 [0]
Given Kudos: 15
Send PM
Re: Four female friends & four male friends will be pictured in [#permalink] New post   31 Jan 2020, 07:48
Bunuel wrote:
Smita04 wrote:
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?

A. 40320
B. 1680
C. 1152
D. 576
E. 70


To meet the condition in the stem men and women should line up either: M-W-M-W-M-W-M-W or W-M-W-M-W-M-W-M. Now, for each of these two cases men can be arranged in 4! ways and women can be arranged also in 4! ways, hence total # of arrangements is 2*4!*4!=1,152.

Answer: C.

Hope it's clear.





Why can't it be 8!/4!*4! = 70?

Can you please explain?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618603 [1]
Given Kudos: 81563
Send PM
CAT Tests Forum Quiz Mode
Re: Four female friends & four male friends will be pictured in [#permalink] New post   31 Jan 2020, 08:07
1
Kudos
Expert Reply
Anurag06 wrote:
Bunuel wrote:
Smita04 wrote:
Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?

A. 40320
B. 1680
C. 1152
D. 576
E. 70


To meet the condition in the stem men and women should line up either: M-W-M-W-M-W-M-W or W-M-W-M-W-M-W-M. Now, for each of these two cases men can be arranged in 4! ways and women can be arranged also in 4! ways, hence total # of arrangements is 2*4!*4!=1,152.

Answer: C.

Hope it's clear.





Why can't it be 8!/4!*4! = 70?

Can you please explain?


8!/(4!*4!) is the number ways to arrange 8 items out of which 4 are of type A and 4 are of type B. For example, the number of ways to arrange 33334444 is 8!/(4!4!).
avatar
S
jim441
Manager
Manager
Joined: 29 Apr 2022
Posts: 203
Own Kudos [?]: 36 [0]
Given Kudos: 277
Location: India
Concentration: Finance, Marketing
GMAT 1: 690 Q48 V35 (Online)
WE:Engineering (Manufacturing)
Send PM
Re: Four female friends & four male friends will be pictured in [#permalink] New post   27 Sep 2022, 16:27
There is some problem with the answer i guess. Correct me if I am wrong.
SO we have 4 boys and 4 girls such that no two boys or no two girls sit togethe.
So we can do this question by gaping method: _B_B_B_B_
We have 5 places for four girls. So we can choose 4 places using 5C4.
Next we can arrange boys and girls in 4!*4! ways.

So the correct answer should be: 5C4*4!*4! = 2880.
User avatar
G
Regor60
Senior Manager
Senior Manager
Joined: 21 Nov 2021
Posts: 437
Own Kudos [?]: 209 [1]
Given Kudos: 343
Send PM
Re: Four female friends & four male friends will be pictured in [#permalink] New post   18 Oct 2022, 13:55
1
Kudos
jim441 wrote:
There is some problem with the answer i guess. Correct me if I am wrong.
SO we have 4 boys and 4 girls such that no two boys or no two girls sit togethe.
So we can do this question by gaping method: _B_B_B_B_
We have 5 places for four girls. So we can choose 4 places using 5C4.
Next we can arrange boys and girls in 4!*4! ways.

So the correct answer should be: 5C4*4!*4! = 2880.



5 places for 4 girls allows 1 place to be unfilled. That one place could be any of the spots between the boys, which would mean two boys sitting next to each other, violating the question stem.

Posted from my mobile device
avatar
S
jim441
Manager
Manager
Joined: 29 Apr 2022
Posts: 203
Own Kudos [?]: 36 [0]
Given Kudos: 277
Location: India
Concentration: Finance, Marketing
GMAT 1: 690 Q48 V35 (Online)
WE:Engineering (Manufacturing)
Send PM
Re: Four female friends & four male friends will be pictured in [#permalink] New post   18 Oct 2022, 14:56
Regor60 wrote:
jim441 wrote:
There is some problem with the answer i guess. Correct me if I am wrong.
SO we have 4 boys and 4 girls such that no two boys or no two girls sit togethe.
So we can do this question by gaping method: _B_B_B_B_
We have 5 places for four girls. So we can choose 4 places using 5C4.
Next we can arrange boys and girls in 4!*4! ways.

So the correct answer should be: 5C4*4!*4! = 2880.



5 places for 4 girls allows 1 place to be unfilled. That one place could be any of the spots between the boys, which would mean two boys sitting next to each other, violating the question stem.

Posted from my mobile device


Thanks a lot, this one my really messing up with me.
GMAT Club Bot
gmatclubot
Re: Four female friends & four male friends will be pictured in [#permalink]
18 Oct 2022, 14:56
Moderators:
Bunuel
Math Expert
92883 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions