SOLUTION: Given 300 marbles and 30 of them are black; what is the probability that if you randomly choose 6 of them (out of the 300) that 3 of them would be black. Request that you show the

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Question 1200862: Given 300 marbles and 30 of them are black; what is the probability that if you randomly choose 6 of them (out of the 300) that 3 of them would be black. Request that you show the steps in the calculation. I know that this is some sort of binomial statistics problem that is probably not simple to solve unless you you the exact formula.
Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
.

The total number of all possible sextuples of 300 marbles is the number of combinations of 300 marbles taken 6 at a time

    C%5B300%5D%5E6 = %28300%2A299%2A298%2A297%2A296%2A295%29%2F%281%2A2%2A3%2A4%2A5%2A6%29 = 962822846700.



The number of all different triples of 30 black marbles is 

    C%5B30%5D%5E3 = %2830%2A29%2A28%29%2F%281%2A2%2A3%29 = 4060.



The number of all different triples of 300-30 = 270 not-black marbles is 

    C%5B270%5D%5E3 = %28270%2A269%2A268%29%2F%281%2A2%2A3%29 = 3244140.



The probability under the problem's question is

    P = %283244140%2A4060%29%2F962822846700 = 0.01368 (rounded).    ANSWER

Solved.

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To see many other similar  (and different)  problems solved,  look into the lesson
    - Elementary Probability problems related to combinations
in this site.