Question

In how many way can $12$ gentlemen sit around a round table so that three specified gentlemen are always together.

• A. $9!$
• B. $10!$
• C. $3!10!$
• D. $3!9!$

Answer 1

Answer: (D)

$3!9!$

Let us consider the $3$ specific gentlemen as a single person that occupies three times the space.

So, now we have $10$ persons who can be made to sit in $9!$ ways and in the space for $3$ gentlemen we can permute them in $3!$ ways.

So, total ways are $3!9!$.