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

 It is currently 07 Dec 2019, 10:11

### 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 4 ladies and 4 gentlemen be

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Sep 2010
Posts: 19
In how many different ways can 4 ladies and 4 gentlemen be  [#permalink]

### Show Tags

04 Oct 2010, 06:40
6
15
00:00

Difficulty:

25% (medium)

Question Stats:

72% (01:23) correct 28% (01:47) wrong based on 368 sessions

### HideShow timer Statistics

In how many different ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?

A. 70
B. 288
C. 576
D. 10,080
E. 20,160
Math Expert
Joined: 02 Sep 2009
Posts: 59588
Re: Ways to sit around the table  [#permalink]

### Show Tags

04 Oct 2010, 08:11
3
10
In how many different ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?

A. 70
B. 288
C. 576
D. 10,080
E. 20,160

Glue the ladies together so that they create one unit, so we would have 5 units: {M1}, {M2}, {M3}, {M4}, and {W1,W2,W3,W4} --> # of different arrangements of $$n$$ objects around the table (circular arrangements) is $$(n-1)!$$, so our 5 objects can be arranged in $$(5-1)!=4!$$ ways.

On the other hand 4 women within their unit also can be arranged in 4! ways --> total $$4!*4!=576$$.

_________________
##### General Discussion
Manager
Joined: 07 Oct 2006
Posts: 54
Location: India
Re: Ways to sit around the table  [#permalink]

### Show Tags

04 Oct 2010, 08:32
Good question... Yet another good explanation from the Master.....
Retired Moderator
Joined: 02 Sep 2010
Posts: 717
Location: London
Re: Ways to sit around the table  [#permalink]

### Show Tags

04 Oct 2010, 08:58
1
In how many different ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?

A. 70
B. 288
C. 576
D. 10,080
E. 20,160

Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways
And there are 4! ways to arrange ladies among themselves

Answer = (4!)^2 = 576 or C
_________________
Manager
Joined: 30 Mar 2013
Posts: 101
Re: In how many different ways can 4 ladies and 4 gentlemen be  [#permalink]

### Show Tags

16 Oct 2014, 02:06
For concept's sake, if we were to do this the opposite way, how would we do it? Say we have (8-1)! of arranging without any conditions. Then it should be 7! - number of ways 2 women can sit together - number of ways three can sit together.

so for number of ways two can sit together I get: (4-1)! and then 4C3 (in how many ways can we place 3 women in 4 slots, since I tied two together * 2)

Number of ways 3 can sit together= seat the men in (4-1)! ways. * 4C2 (in how many ways can two women be placed in 4 slots, since I tied three women together this time)*3! (for the number of arrangements of three women ties together)

This doesn't give me the correct answer. Where have I gone wrong?
Non-Human User
Joined: 09 Sep 2013
Posts: 13723
Re: In how many different ways can 4 ladies and 4 gentlemen be  [#permalink]

### Show Tags

05 Mar 2019, 06:52
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 4 ladies and 4 gentlemen be   [#permalink] 05 Mar 2019, 06:52
Display posts from previous: Sort by