Four married couples are to be seated around a circulartable. The hostess wants

Question

Four married couples are to be seated around a circulartable. The hostess wants to know how many ways she can arrange thecouples around the table... a)if there are no restrictions? b)if each husband must sit beside his wife? c)if each husbandmust sit beside his wife and men and womenalternate? d)if each husband sits opposite his wife? Four married couples are to be seated around a circulartable. The hostess wants to know how many ways she can arrange thecouples around the table... a)if there are no restrictions? b)if each husband must sit beside his wife? c)if each husbandmust sit beside his wife and men and womenalternate? d)if each husband sits opposite his wife?

Explanation / Answer

Four married couples means 8 individuals. a) if there are no restrictions, they can be seated around atable in (8-1)! = 7! ways = 5040 ways b)if each husband must sit beside his wife. hence we canconsider a couple as 1 unit. hence we have 4 units to be seatedaround a table. each unit can get themselves internallyarranged in 2 ! ways = 2 ways hence no of ways in which this arrangement is possible =(4-1)! x 2 x 2 x 2 x 2 = 96 ways c)if each husband must sit beside his wife and men and womenalternate? hence we can consider a couple as 1 unit. hence we have 4units to be seated around a table. all unit can getthemselves internally arranged in 2 ! ways = 2 ways hence no of ways in which this arrangement is possible =(4-1)! x 2 = 12 ways b)if each husband must sit beside his wife. hence we canconsider a couple as 1 unit. hence we have 4 units to be seatedaround a table. each unit can get themselves internallyarranged in 2 ! ways = 2 ways hence no of ways in which this arrangement is possible =(4-1)! x 2 x 2 x 2 x 2 = 96 ways c)if each husband must sit beside his wife and men and womenalternate? hence we can consider a couple as 1 unit. hence we have 4units to be seated around a table. all unit can getthemselves internally arranged in 2 ! ways = 2 ways hence no of ways in which this arrangement is possible =(4-1)! x 2 = 12 ways

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