Last visit was: 06 Oct 2024, 10:26 It is currently 06 Oct 2024, 10:26
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
avatar
Joined: 01 Sep 2010
Posts: 19
Own Kudos [?]: 272 [47]
Given Kudos: 8
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 95949
Own Kudos [?]: 665707 [23]
Given Kudos: 87511
Send PM
General Discussion
User avatar
Joined: 07 Oct 2006
Posts: 45
Own Kudos [?]: 20 [0]
Given Kudos: 3
Location: India
Send PM
User avatar
Retired Moderator
Joined: 02 Sep 2010
Posts: 611
Own Kudos [?]: 3003 [1]
Given Kudos: 25
Location: London
 Q51  V41
Send PM
Re: Ways to sit around the table [#permalink]
1
Bookmarks
eladshush
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
Joined: 30 Mar 2013
Posts: 78
Own Kudos [?]: 199 [0]
Given Kudos: 197
Location: United States
GMAT 1: 760 Q50 V44
Send PM
Re: In how many different ways can 4 ladies and 4 gentlemen be [#permalink]
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?
Joined: 11 Aug 2020
Posts: 1232
Own Kudos [?]: 217 [1]
Given Kudos: 332
Send PM
Re: In how many different ways can 4 ladies and 4 gentlemen be [#permalink]
1
Bookmarks
_ _ _ _ _ _ _ _ <---- 8 spots

Combination:
Since the four women must be together there is 4C4 ways we can choose seats for them.

Permutation:
Among the women, there are 4! ways we can arrange them.
Likewise among men there are 4! ways that they can be arranged

4! x 4! = 576.

Answer is C.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 35123
Own Kudos [?]: 890 [0]
Given Kudos: 0
Send PM
Re: In how many different ways can 4 ladies and 4 gentlemen be [#permalink]
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 Bot
Re: In how many different ways can 4 ladies and 4 gentlemen be [#permalink]
Moderator:
Math Expert
95949 posts