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20 Apr 2012, 17:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (00:49) correct
35%
(01:02)
wrong
based on 381
sessions
History
Date
Time
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Not Attempted Yet
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!
A. 4!
B. 5!
C. 4!*4!
D. 5!*4!
E. 5!*5!
12 Jul 2012, 01:39
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manasrastogi
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.
General Discussion
21 Apr 2012, 00:00
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keiraria
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.
