SOLUTION: The number of ways to arrange the seating of four men and their wives around a circle, so that each man remains adjacent to his wife, equals..."
Followed by the multiple-choice
Algebra.Com
Question 1209231: The number of ways to arrange the seating of four men and their wives around a circle, so that each man remains adjacent to his wife, equals..."
Followed by the multiple-choice options:
48
96
120
384
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
(1) Treat each husband-wife pair as a single unit. You then have four things to arrange around the table.
(2) If they were being arranged in a line, the number of ways of arranging them would be 4*3*2*1 = 4! = 24. But since they are being arranged around a table, there are four possible "starting points" for the arrangement, so the number of ways to arrange the four groups around a table is 24/4 = 6. (In general, there are (n!) ways of arranging n things in a line and ((n-1)!) ways of arranging n items in a circular pattern.)
(3) Within each of the four groups, the man and woman can be in either of two orders.
ANSWER: (6)(2)(2)(2)(2) = 96
RELATED QUESTIONS
Five men and their five wives were invited to a graduation ceremony for high school... (answered by 41 years)
Four men and their wives sit on a bench.in how many ways can they be... (answered by ewatrrr)
If a man has eight pens. Four are black, three are blue, and one is red. How many... (answered by gotpork1)
a family has a man, his wife,their four sons and their wives l. the family of every son... (answered by josmiceli)
number of ways of selecting 4 men from the row of 10 men such that no two are adjacent to (answered by Finavon)
As I was going to St. Ives, I met a man with 7 wives, every wife had 7 sacks, and every... (answered by KMST)
Find the number of ways of seating 3 men and 5 women in a row if there is no... (answered by ewatrrr)
A journal polled its readers to determine the proportion of wives who, if given a second... (answered by FrankM)
The number of ways to arrange 4 green balls, 3 red balls, and 2 white balls in a straight (answered by ikleyn)