Question

A group of $10$ persons including ''Manager'', ''Assistant manager'' and ''Secretary'' are to be seated around a circular table.
The total number of possible arrangements, if ''Manager'' and ''Secretary'' had to sit together and ''Assistant manager'' had to sit opposite to ''Manager'' is

• A. $2\times 8!$
• B. $8!$
• C. $2\times 7!$
• D. $3\times 8!$

Answer 1

The correct option is C $2\times 7!$

Let the ''Manager'' be seated first, since it is a circular table ''Manager'' can be seated in only $1$ way.
Now the ''Secretary'' has to sit opposite to ''Manager'', it can be done in only $1$ way.
Now the ''Assistant manager'' had to sit together with ''Manager'', it can be done in only $2$ ways.


Now the remaining persons can be arranged in $7!$ ways.
$\therefore$ The total possible arrangements is $=1\times 1\times 2\times 7!$