Answer to Question #50620 in Combinatorics | Number Theory for tinu

Question

there are 5 students of department A and 5 of department B.how many arrangement are possible around a circular table where 2 students of department B will not sit beside?

i solve this like this.

students of department B can sit at the middle of 2 students of department A. so there are 5 empty places between the students of department A. so in this 5 place 5 students of department B can sit in 5! Ways.
and the students of department A can change their position in (5-1)! =4! ways.

so in total it is 5!*4!. that's it. my question is we know in circular permutation its (n-1)!. so i do (5-1)! for department A students. why it is not done for department B students. they also in a circle. please explain