SOLUTION: 13 pupils have to be divided into three groups of 4,5 and 4..in how many ways can this be dan?

If the 13 pupils are A,B,C,D,E,F,G,H,I,J,K,L,M

First consider the three groups to be Group A of 4, Group B of 5, and
Group C of 4.

Choose the pupils for Group A:
That's 13 pupils choose 4, or 13C4

Choose the pupils for Group B:
That's 9 remaining pupils choose 5, or 9C5

Choose the pupils for Group C:
That's 4 remaining pupils choose 4, or 4C4

That would be (13C4)(9C4)(4C4) = (715)(126)(1) = 90090

if such groupings as these 2:

Group A = {C,G,I,M}, Group B = {B,D,E,J,L}, Group C ={A,F,H,K}    

and 

Group A = {A,F,H,K}, Group B = {B,D,E,J,L}, Group C ={C,G,I,M}

were distinguishable (with Groups A and C swapped).

But they probably aren't, so we will divide 90090 by 2 and get

Answer = 45045.

Edwin