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 specific conditions,we treat the Chairman,Secretary,and Deputy Secretary as a single block.Si

Vedclass · Accepted Answer

$2 	imes 12!$

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(A) To arrange $15$ members around a circular table with specific conditions,we treat the Chairman,Secretary,and Deputy Secretary as a single block.Since the Secretary and Deputy Secretary must sit on either side of the Chairman,the block can be arranged in $2! = 2$ ways (Secretary-Chairman-Deputy Secretary or Deputy Secretary-Chairman-Secretary).After grouping these $3$ members into $1$ unit,we have $15 - 3 + 1 = 13$ units to arrange in a circle.The number of ways to arrange $n$ objects in a circle is $(n-1)!$.Here,$n = 13$,so the number of circular arrangements is $(13-1)! = 12!$.Considering the internal arrangement of the block,the total number of ways is $2 	imes 12!$.

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

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