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!

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

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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)

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