Question

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

• A. $6!6!$
• B. $5!6!$
• C. $5!5!$
• D. $6\times 5$

Answer 1

The correct option is B $5!6!$

Fix up one student and remaining 5 students can be seated in 5! ways. Now 6 teachers are to be arranged between these 6 students and number of arrangements will be 6! ways.

Hence by fundamental theorem the total number of ways is $5!6!$

Hence the answer is B.