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(13198)   (Show Source):
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(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
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