In how many ways can 15 members of a council | vedclass

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(A) To arrange $15$ members around a circular table with the condition that the Secretary and Deputy Secretary sit on either side of the Chairman,we t

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$2 	imes 12!$

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(A) To arrange $15$ members around a circular table with the condition that the Secretary and Deputy Secretary sit on either side of the Chairman,we treat the group of these $3$ members as a single unit.This leaves us with $15 - 3 + 1 = 13$ units to arrange in a circle.The number of ways to arrange $13$ units in a circle is $(13 - 1)! = 12!$.Within the unit of $3$ members,the Secretary and Deputy Secretary can swap places on either side of the Chairman in $2! = 2$ ways.Therefore,the total number of arrangements is $12! 	imes 2$.

In how many ways can $15$ members of a council sit along a circular table,when the Secretary is to sit on one side of the Chairman and the Deputy Secretary on the other side?

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