Looking at the categories:

A: 4/15

B: 5/15

C: 6/15

Now, looking at these possible outcome combinations: C,C,N ; C,N,C ; or N,C,C. (N denoting "not C" in this case.)

This would be a simple binominal IF it were done with replacement:

But since there is no replacement, each succeeding factor is conditional to the previous factor (i.e. you simply remove what you take out at each step):

Where 9/13 is the "not C" part, i.e. 4/13 + 5/13