I will use a symbol F            as a placeholder for female teachers;
           a symbol G (as girls) as a placeholder for female students;
           a symbol B (as boys)  as a placeholder for male students.


As problem is worded, the only way to satisfy requirements is to have a block
FGFGF at circular siting.


Also, I will use a symbol D for this block FGFGF, when I will consider this block as one clued object.


Then 

    - there are 3! = 6 ways/permutations for 3 distinguished female teachers (F) inside this block; 

    - there are 2! = 2 ways/permutations for 2 distinguished female students (G) inside this block;

   -  in circular sitting, we can assume that the block D = FGFGF is in position "North", or 12 o'clock.
      
      Then in circular sitting, there is only one possible remaining configuration  DGG, or  FGFGFBB.

       Finally, since 2 permutations are possible for two distinguishable boys, it gives an additional factor 2.


Now the number of all possible arrangements is 3! * 2! * 2! = 6*2*2 = 24.    ANSWER

It has to be like this:



2! ways to seat the MS's, the male students.
3! ways to seat the FT's, the female teachers.
2! ways to seat the FS's, the female students.

(2!)(3!)(2!) =(2)(6)(2) = 24 ways.

Edwin