find the probabilities for each case and add them up

by (all possible) cases, i mean:

probability of choosing 1 white, 0 black, 1 blue, 1 red, 3 green

probability of choosing 1 white, 0 black, 0 blue, 2 red, 3 green

probability of choosing 1 white, 0 black, 2 blue, 0 red, 3 green

.

.

.

.

or we could do:

1 - probability of choosing no white and no black ball

so all you have to worry about are the number of ways you can choose 6 balls among the three remaining colors. there is a formula for that sort of thing. can't remember right now, i'll have to look it up. but when you do get it, just multiply the answer by 0.2 and that will give you the probability of choosing no white and no black ball