GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 03 Aug 2020, 22:15

### 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

# 4 couples are seating at a round tables how many ways can

Author Message
Intern
Joined: 05 Apr 2012
Posts: 38
4 couples are seating at a round tables how many ways can  [#permalink]

### Show Tags

20 Apr 2012, 16:07
3
00:00

Difficulty:

(N/A)

Question Stats:

75% (00:41) correct 25% (01:55) wrong based on 17 sessions

### HideShow timer Statistics

4 couples are seating at a round tables how many ways can the 4 women sit together

I am trying to understand circular permutation
Math Expert
Joined: 02 Sep 2009
Posts: 65771

### Show Tags

20 Apr 2012, 23:00
keiraria wrote:
hello

4 couples are seating at a round tables
how many ways can the 4 women sit together

best regards

I am trying to understand circular permutation

4 men can be arranged around a table in (4-1)!=3! ways;

Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.

So, total # of ways is 3!*4*4!=4!*4!

Another way: if 4 women sit together around a table then 4 men also sit together, so total # of arrangements is 4!*4!.

Check this for circular arrangements: math-combinatorics-87345.html

Hope it helps.
_________________
Intern
Joined: 21 Jun 2012
Posts: 2

### Show Tags

11 Jul 2012, 21:46
Can we put all the women in 1 group.
Total will be : 4 men + 1 group of women = 5
To arrange these 5, we will have 5! ways.
Again to group all the women we will have = 4! ways.
Then total ways = 5! X 4!
Math Expert
Joined: 02 Sep 2009
Posts: 65771

### Show Tags

12 Jul 2012, 00:39
manasrastogi wrote:
Can we put all the women in 1 group.
Total will be : 4 men + 1 group of women = 5
To arrange these 5, we will have 5! ways.
Again to group all the women we will have = 4! ways.
Then total ways = 5! X 4!

The red part is not correct.

Notice that we have circular not linear arrangement.

The difference between placement in a row and that in a circle is following: if we shift all object by one position, we will get different arrangement in a row but the same relative arrangement in a circle. So, for the number of circular arrangements of n objects we have: $$\frac{n!}{n}=(n-1)!$$.

Hence 4 men and 1 group of four women (total of 5 units) can be arranged around a circular table in (5-1)!=4! ways. Next, these 4 women within their unit can be arranged in 4! ways, which gives total equal to 4!*4!.

at-a-party-5-people-are-to-be-seated-around-a-circular-104101.html
seven-family-members-are-seated-around-their-circular-dinner-102184.html
seven-men-and-seven-women-have-to-sit-around-a-circular-11473.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
seven-men-and-five-women-have-to-sit-around-a-circular-table-98185.html
a-group-of-8-friends-sit-together-in-a-circle-alice-betty-106928.html
find-the-number-of-ways-in-which-four-men-two-women-and-a-106919.html

Hope it helps.
_________________
Intern
Joined: 21 Jun 2012
Posts: 2
Re: 4 couples are seating at a round tables how many ways can  [#permalink]

### Show Tags

12 Jul 2012, 01:20
Thanks Bunuel.....
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10782
Location: Pune, India
Re: 4 couples are seating at a round tables how many ways can  [#permalink]

### Show Tags

12 Jul 2012, 20:47
1
Check out these posts for fundamentals of circular arrangements:

http://www.veritasprep.com/blog/2011/10 ... angements/
http://www.veritasprep.com/blog/2011/10 ... ts-part-i/
http://www.veritasprep.com/blog/2011/11 ... 3-part-ii/
_________________
Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 15593
Re: 4 couples are seating at a round tables how many ways can  [#permalink]

### Show Tags

13 Apr 2019, 22:06
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: 4 couples are seating at a round tables how many ways can   [#permalink] 13 Apr 2019, 22:06