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)