Question

Six teachers and six students have to sit around a circular table such that there is a teacher between any two students. The number of ways in which they can sit is

• A. $6!\times 6!$
• B. $5!\times 6!$
• C. $5!\times 5!$
• D. None of these

Answer 1

The correct option is B

$5!\times 6!$

Explanation for the correct answer:

Finding the number of ways of arranging students and teachers:

Six students are to be arranged around a circular table.

The number of ways in which the students can be arranged is given by

$$\begin{gathered} \left(n-1\right)!=(6-1)! \\ =5! \end{gathered}$$

Therefore, the students can be seated in $5!$ways.

Among these $6$ students, there are six vacant places for the teachers.

The number of ways in which the teachers can be seated is given by

$n!=6!$

Therefore, the teachers can be seated in $6!$ ways.

Hence, the number of seating arrangements $=5!\times 6!$

Therefore, option (B) is the correct answer.