Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Aug 2014, 21:09

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The number of ways in which 5 men and 6 women can be seated

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 24 Mar 2010
Posts: 78
Location: Mumbai, India
Schools: INSEAD - dinged; IE-admit; ISB - admit; IIMB-admit; SPJain- admit; IIM C- Admit, IIM A - Dinged after interview. Finally joining IIM B
WE 1: 3
WE 2: 2
WE 3: 2
Followers: 4

Kudos [?]: 11 [0], given: 9

The number of ways in which 5 men and 6 women can be seated [#permalink] New post 27 May 2010, 20:30
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (02:20) wrong based on 1 sessions
The number of ways in which 5 men and 6 women can be seated

1. In a row
2. Around a table, such that no two men or women are together.
_________________

ASHISH DONGRE
BE KIND & GENEROUS TO SHARE THE KUDOS...THE MORE YOUR GIVE THE MORE YOU GET

Manager
Manager
avatar
Joined: 20 Apr 2010
Posts: 154
Location: I N D I A
Followers: 3

Kudos [?]: 15 [0], given: 16

Re: please help with the Seating arrangement problems [#permalink] New post 27 May 2010, 23:29
No of way in which 5 men and 6 women can be seated in a row = 6! * 5! as first has to be a woman then man then woman then man n so on...
Manager
Manager
avatar
Joined: 16 Mar 2010
Posts: 191
Followers: 2

Kudos [?]: 38 [0], given: 9

GMAT Tests User
Re: please help with the Seating arrangement problems [#permalink] New post 28 May 2010, 00:18
Please post the OA.
I am providing my thinking below.
Seating arrangement in a row = 6! * 5!
Seating arrangement in a table = 5! * 5!
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24326 [1] , given: 2676

Re: please help with the Seating arrangement problems [#permalink] New post 28 May 2010, 02:02
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
meghash3 wrote:
No of way in which 5 men and 6 women can be seated 1) in a row 2 ) around a table, such that no two men or women are together.


(1) In how many different ways 5 men and 6 women can be seated in row so that no 2 women or 2 men are together?

# of ways 6 women can be seated in a row is 6!. If men will be seated between them (there will be exactly 5 places between women) no 2 men or 2 women will be together. # of ways 5 men can be seated in a row is 5!. So total 6!*5!.

(2) In how many different ways 5 men and 6 women can be seated around the table so that no 2 women or 2 men are together?

Zero. 6 women around the table --> 6 places between them and only 5 men, so in any case at least 2 women will be together.

If the question were: "In how many different ways 6 men and 6 women can be seated around the table so that no 2 women or 2 men are together?"

Then: 6 men around the table can be seated in (6-1)!=5! # of ways (# of circular permutations of n different objects is (n-1)!). 6 women between them can be seated in 6! # of ways. Total: 5!6!.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 01 Apr 2010
Posts: 14
Followers: 0

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

Re: please help with the Seating arrangement problems [#permalink] New post 28 May 2010, 03:04
Row = 5! * 6!
Circle = 0 (men can be separated from each other with a woman in between but the 6th woman invariably sits next to the 1st woman) Pls correct my understanding if its wrong :?
Manager
Manager
avatar
Joined: 24 Mar 2010
Posts: 78
Location: Mumbai, India
Schools: INSEAD - dinged; IE-admit; ISB - admit; IIMB-admit; SPJain- admit; IIM C- Admit, IIM A - Dinged after interview. Finally joining IIM B
WE 1: 3
WE 2: 2
WE 3: 2
Followers: 4

Kudos [?]: 11 [0], given: 9

Re: please help with the Seating arrangement problems [#permalink] New post 28 May 2010, 06:49
Thanks all and Bunuel. That is the OA.

I have a doubt still..
Wont we multiply 6!5! by 2!, as there are two possibilities, one we fix women in first position and other that we fix a man in hte first position?

Bunuel wrote:
meghash3 wrote:
No of way in which 5 men and 6 women can be seated 1) in a row 2 ) around a table, such that no two men or women are together.


(1) In how many different ways 5 men and 6 women can be seated in row so that no 2 women or 2 men are together?

# of ways 6 women can be seated in a row is 6!. If men will be seated between them (there will be exactly 5 places between women) no 2 men or 2 women will be together. # of ways 5 men can be seated in a row is 5!. So total 6!*5!.

(2) In how many different ways 5 men and 6 women can be seated around the table so that no 2 women or 2 men are together?

Zero. 6 women around the table --> 6 places between them and only 5 men, so in any case at least 2 women will be together.

If the question were: "In how many different ways 6 men and 6 women can be seated around the table so that no 2 women or 2 men are together?"

Then: 6 men around the table can be seated in (6-1)!=5! # of ways (# of circular permutations of n different objects is (n-1)!). 6 women between them can be seated in 6! # of ways. Total: 5!6!.

Hope it helps.

_________________

ASHISH DONGRE
BE KIND & GENEROUS TO SHARE THE KUDOS...THE MORE YOUR GIVE THE MORE YOU GET

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24326 [0], given: 2676

Re: please help with the Seating arrangement problems [#permalink] New post 28 May 2010, 07:46
Expert's post
meghash3 wrote:
Thanks all and Bunuel. That is the OA.

I have a doubt still..
Wont we multiply 6!5! by 2!, as there are two possibilities, one we fix women in first position and other that we fix a man in hte first position?


It's only possible woman to be first and than man: W-M-W-M-W-M-W-M-W-M-W (remember there are 6 women and 5 men).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 21 Jul 2010
Posts: 4
Followers: 0

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

Re: please help with the Seating arrangement problems [#permalink] New post 31 Jul 2010, 02:56
I know this post is a bit old...but it just caught my eye now :)

I have a Q, Bunuel

Since its 6 W & 5 M in a circular pattern, there will b 6 slots to choose from for the 5 M

Hence it will b 6C5 X 5! X 5!, won't it?
Intern
Intern
avatar
Joined: 09 Dec 2008
Posts: 29
Location: Vietnam
Schools: Somewhere
Followers: 0

Kudos [?]: 9 [0], given: 2

Re: please help with the Seating arrangement problems [#permalink] New post 31 Jul 2010, 23:28
Bunuel wrote:
meghash3 wrote:
No of way in which 5 men and 6 women can be seated 1) in a row 2 ) around a table, such that no two men or women are together.


(1) In how many different ways 5 men and 6 women can be seated in row so that no 2 women or 2 men are together?

# of ways 6 women can be seated in a row is 6!. If men will be seated between them (there will be exactly 5 places between women) no 2 men or 2 women will be together. # of ways 5 men can be seated in a row is 5!. So total 6!*5!.

(2) In how many different ways 5 men and 6 women can be seated around the table so that no 2 women or 2 men are together?

Zero. 6 women around the table --> 6 places between them and only 5 men, so in any case at least 2 women will be together.

If the question were: "In how many different ways 6 men and 6 women can be seated around the table so that no 2 women or 2 men are together?"

Then: 6 men around the table can be seated in (6-1)!=5! # of ways (# of circular permutations of n different objects is (n-1)!). 6 women between them can be seated in 6! # of ways. Total: 5!6!.

Hope it helps.


It's really clear. Thanks for new knowledge!
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 184
Followers: 0

Kudos [?]: 18 [0], given: 25

Re: The number of ways in which 5 men and 6 women can be seated [#permalink] New post 02 Sep 2013, 03:06
Bunuel, is my thinking correct for No2?

total: Number of possible sitting arrangements in a circular table: 10! (11-1)!

restriction:
Taking 2 men as a set who are not allowed to sit next to each other: 2!
Taking 2 women as a set who are not allowed to sit next to each other: 2!
The rest of the sitting arrangements is 6! (7-1)!

So,
total - restriction = 10! - (2! + 2! + 6!) = 0.
Intern
Intern
User avatar
Joined: 07 Jan 2013
Posts: 26
Location: Poland
GPA: 3.8
Followers: 0

Kudos [?]: 5 [0], given: 491

Re: please help with the Seating arrangement problems [#permalink] New post 14 Oct 2013, 20:06
Bunuel wrote:
meghash3 wrote:
No of way in which 5 men and 6 women can be seated 1) in a row 2 ) around a table, such that no two men or women are together.


(1) In how many different ways 5 men and 6 women can be seated in row so that no 2 women or 2 men are together?

# of ways 6 women can be seated in a row is 6!. If men will be seated between them (there will be exactly 5 places between women) no 2 men or 2 women will be together. # of ways 5 men can be seated in a row is 5!. So total 6!*5!.

(2) In how many different ways 5 men and 6 women can be seated around the table so that no 2 women or 2 men are together?

Zero. 6 women around the table --> 6 places between them and only 5 men, so in any case at least 2 women will be together.

If the question were: "In how many different ways 6 men and 6 women can be seated around the table so that no 2 women or 2 men are together?"

Then: 6 men around the table can be seated in (6-1)!=5! # of ways (# of circular permutations of n different objects is (n-1)!). 6 women between them can be seated in 6! # of ways. Total: 5!6!.

Hope it helps.


Hi Banuel! Why the solution is not 5!*6*5!?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19020
Followers: 3358

Kudos [?]: 24326 [0], given: 2676

Re: please help with the Seating arrangement problems [#permalink] New post 15 Oct 2013, 08:52
Expert's post
Magdak wrote:
Bunuel wrote:
meghash3 wrote:
No of way in which 5 men and 6 women can be seated 1) in a row 2 ) around a table, such that no two men or women are together.


(1) In how many different ways 5 men and 6 women can be seated in row so that no 2 women or 2 men are together?

# of ways 6 women can be seated in a row is 6!. If men will be seated between them (there will be exactly 5 places between women) no 2 men or 2 women will be together. # of ways 5 men can be seated in a row is 5!. So total 6!*5!.

(2) In how many different ways 5 men and 6 women can be seated around the table so that no 2 women or 2 men are together?

Zero. 6 women around the table --> 6 places between them and only 5 men, so in any case at least 2 women will be together.

If the question were: "In how many different ways 6 men and 6 women can be seated around the table so that no 2 women or 2 men are together?"

Then: 6 men around the table can be seated in (6-1)!=5! # of ways (# of circular permutations of n different objects is (n-1)!). 6 women between them can be seated in 6! # of ways. Total: 5!6!.

Hope it helps.


Hi Banuel! Why the solution is not 5!*6*5!?


Can you please elaborate what you mean?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: please help with the Seating arrangement problems   [#permalink] 15 Oct 2013, 08:52
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic In how many ways can a commitee of 4 women and 5 men rajathpanta 4 24 Aug 2012, 08:02
1 Experts publish their posts in the topic Find the number of ways in which four men, two women and a subhashghosh 10 26 Dec 2010, 07:39
Find the number of ways in which 5 men and 4 women can be mahesh004 7 26 May 2006, 04:43
In how many ways can 5 men and 5 women be seated in a krishrads 4 02 Jun 2005, 09:58
In how many ways can 3 men and 3 women be seated around a swath20 11 05 Jan 2005, 07:41
Display posts from previous: Sort by

The number of ways in which 5 men and 6 women can be seated

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.