In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together?

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!

Tardigrade Admin · Accepted Answer

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 !.

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

9!

10!

3! 10!

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 $3! 9!$ .

Q. In how many ways can 12 gentlemen sit around a round table so that three specified gentlemen are always together?

9!

10!

3! 10!

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!.

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

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 $3! 9!$ .