Question

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

• A. $9!$
• B. $8!$
• C. $3!\times 8!$
• D. $3!\times 7!$

Answer 1

The correct option is D $3!\times 7!$

Considering ''Manager'', ''Assistant manager'' and ''Secretory'' as single unit, then total different units present will be $7+1=8$
They can be arranged in $(8-1)!=7!$ ways.
As ''Manager'', ''Assistant manager'' and ''Secretory'' can interchange among themselves in $3!$ ways
$\therefore$Total number of required ways $=7!\times 3!$