Oh! Now I get it. C(4,1) x C(6,3) x C(3,1) x C(3,1) x C(3,1) divided by 4^6 is not right, because if one of the student picks 1 among three, the leftover would be two.
So. C(4,1) x C(6,3) x C(3,1) x C(2,1) x C(1,1) divided by 4^6
And Have I got right in the event b?