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

Question

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

A. 4!
B. 5!
C. 4!*4!
D. 5!*4!
E. 5!*5!

Bunuel · Accepted Answer

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!. Questions about this concept to practice: in-how-many-different-ways-can-4-ladies-and-4-gentlemen-be-102187.html 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.

Bunuel · Answer

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.

manasrastogi · Answer

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!

manasrastogi · Answer

Thanks Bunuel.....
I got it and thanks for posting additional links for practice.

KarishmaB · Answer

Check out posts on this concept on the blog link given in my signature below.

Shinz · Answer

we put all the women in 1 group.
Total will be : 4 men + 1 group of 4 women = 5
To arrange these 5 in a circular table, we will have 4! ways.
Again to group all the women we will have = 4! ways.
Then total ways = 4! X 4!

MrMaxMan · Answer

I found it easiest to answer this question by bundling all the women together.
<W,W,W,W,M,M,M,M> = 8
<[W,W,W,W],M,M,M,M> = 5
Since it's a circular arrangement and shifting everone one way will be the same order, each person shifted accounts for one of the same orders, so basically we just have to remove that.
If there were 5! ways to arrange them in a straight line, there is n!/n ways to arrange them around a circle. You can visualize this by "pinning" one person that everyone is referenced to.
In this case it would be 5!/5 = (5-1)! = 4! ways to arrange all people, then 4! ways to arrange the women in their own group. We don't "pin" any of the women because we already removed the duplicates from the total group.
Total ways = 4!*4!

keiraria

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

A. 4!
B. 5!
C. 4!*4!
D. 5!*4!
E. 5!*5!

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards