Question

In how many ways 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!

Answer 2

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 $3 !\, 9 !$.

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