12 persons are to be arranged at a round tabl | vedclass

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(A) The total number of ways to arrange $12$ persons around a round table is $(12 - 1)! = 11!$.To find the number of arrangements where $2$ particular

Vedclass · Accepted Answer

$9(10!)$

Vedclass · Answer

(A) The total number of ways to arrange $12$ persons around a round table is $(12 - 1)! = 11!$.To find the number of arrangements where $2$ particular persons sit side by side,we treat them as a single unit. Now,we have $11$ units to arrange in a circle,which can be done in $(11 - 1)! = 10!$ ways. Within the unit,the $2$ persons can be arranged in $2!$ ways.So,the number of ways where $2$ particular persons sit together is $10! 	imes 2! = 2 	imes 10!$.The number of arrangements where they are not side by side is the total arrangements minus the arrangements where they are together:$11! - (2 	imes 10!) = (11 	imes 10!) - (2 	imes 10!) = (11 - 2) 	imes 10! = 9 	imes 10!$.

$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

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