The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is

The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in  $7P6$ways. 7 teachers can sit in (7-1)! ways.

 Required no.of ways is =  $7P6.6! = 7!.6!$