Can someone explain how to do this:

Question

There are 100 boys , 80 girls, and 20 teachers.
Out of these, how many ways can 2 girls, 2 boys and 1 teacher (all together in a group of 5) be chosen?

Answer 1

How many ways can 2 girls be chosen from 80?
n = 80
r = 2
C(n,r) = n!/[r!(n-r)!]
= 80!/[2!(78!)] 80*79/2 = 3160
then 2 boys from 100
100*99/2 = 4950
then 1 teacher from 20 is obviously 20
I now have 3160 groups of girls, 4950 groups of boys and 20 groups of teachers.
The ways of getting a particular group
of girls are 3160
the ways of combining that group of girls with a particular group of boys are 3160*4950
then the ways of combining a particular group of girls and boys with a particular teacher are 3160*4950*20