Question 1172463
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We consider unordered subsets.


The number of all possible unordered 8-marble subsets is  {{{C[60]^8}}} = {{{(60*59*58*57*56*55*54*53)/(1*2*3*4*5*6*7*8)}}} = 2558620845.


It is the total space of events in this problem.


The number of all favorable unordered subsets consisting of 2 white and 6 black marbles is  {{{C[30]^2}}}.{{{C[30]^6}}} = 453*593775 = 258292125.


The probability under the problem's question is  P = {{{favorable/total}}} = {{{258292125/2558620845}}} = 0.10095.      <U>ANSWER</U>
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Solved.