If 12 people are to be seated around a circul | vedclass

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(A) The total number of ways to arrange $12$ people around a circular table is $(12-1)! = 11!$. To find the number of ways where two specific individu

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$9(10!)$

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(A) The total number of ways to arrange $12$ people around a circular table is $(12-1)! = 11!$. To find the number of ways where two specific individuals sit together,we treat them as a single unit. This leaves us with $11$ units to arrange in a circle,which can be done in $(11-1)! = 10!$ ways. Since the two individuals can swap places between themselves,they can be arranged in $2! = 2$ ways. Thus,the number of ways they sit together is $2 	imes 10!$. The number of ways they do not sit together is the total arrangements minus the arrangements where they sit together: $11! - 2 	imes 10! = 11 	imes 10! - 2 	imes 10! = (11-2) 	imes 10! = 9 	imes 10!$.

If $12$ people are to be seated around a circular table,in how many ways can they be seated such that two specific individuals do not sit together?

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