There are B = 8 R = 4 G = 3 total = T = 15
Let three marbles be chosen one after another. It does not matter we select one after another or all three marbles at the same time, as long as we do not look at them till we have all three. We use the conditional probability formula for dependent events A and B.
P ( B ) = P(B/A) * P(A)
P ( Blue, Blue, Blue) = B / T * (B-1) / (T-1) * (B-2) / (T-2)
= 8/15 * 7/14 * 6/13 = 8 / 65
There are six possible ways in which this can happen.
The selections can be : BRG, BGR, RBG, RGB, GBR, GRB - in this order. But which ever order of selection we choose the probabilities will be, for each of them :
B/T * G/ (T-1) * R / (T-2) or B*G*R / [ T (T-1)(T-2) ]
So the answer is = 6 * (8 * 4 * 3) / [ 15 * 14 * 13 ] = 96/455