SOLUTION: A bag contains 30 white marbles and 30 black marbles. If 8 marbles are chosen, what is the probability that there will be 2 white marbles and 6 black marbles?

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Question 1172463: A bag contains 30 white marbles and 30 black marbles. If 8 marbles are chosen,
what is the probability that there will be 2 white marbles and 6 black marbles?

Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
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We consider unordered subsets.


The number of all possible unordered 8-marble subsets is  C%5B60%5D%5E8 = %2860%2A59%2A58%2A57%2A56%2A55%2A54%2A53%29%2F%281%2A2%2A3%2A4%2A5%2A6%2A7%2A8%29 = 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%5B30%5D%5E2.C%5B30%5D%5E6 = 453*593775 = 258292125.


The probability under the problem's question is  P = favorable%2Ftotal = 258292125%2F2558620845 = 0.10095.      ANSWER

Solved.