So this formula does not work?
nCr
C = combination
n = total number of ojects that you can choose from
r = the number that you need to choose
1blackball and 2 nonblack b***s + 2blackballs and 1 nonblack ball + 3blackballs and 0 nonblack b***s
(3C1)(6C2)+(3C2)(6C1)+(3C3)(6C0)