In a party,12 persons are to be arranged arou | vedclass

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(A) The total number of ways to arrange $12$ persons around a round table is given by $(n-1)!$,where $n=12$.Total arrangements $= (12-1)! = 11!$.Next,

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$9 	imes 10 !$

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(A) The total number of ways to arrange $12$ persons around a round table is given by $(n-1)!$,where $n=12$.Total arrangements $= (12-1)! = 11!$.Next,we calculate the number of ways where $2$ particular persons sit side by side. We treat these $2$ persons as a single unit. Now,we have $11$ units to arrange around a round table,which can be done in $(11-1)! = 10!$ ways.Since the $2$ persons within the unit can be arranged in $2!$ ways,the total number of ways where they sit together is $10! 	imes 2!$.Finally,the number of arrangements where the $2$ particular persons do not sit side by side is the total arrangements minus the arrangements where they sit together:$= 11! - (10! 	imes 2!)$$= (11 	imes 10!) - (2 	imes 10!)$$= (11-2) 	imes 10!$$= 9 	imes 10!$

In a party,$12$ persons are to be arranged around a round table. If two particular persons are not to be seated side by side,then the total number of arrangements is

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