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If you have $10$ red marbles and $15$ green marbles in a bag, and you randomly choose $6$, what is the probability that $5$ red marbles will be selected?

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Is this the probability that exactly $5$ marbles are selected or $5$ or more marbles are selected? Is this a homework problem? (It is absolutely OK if it is, we just need to tag it as such.) –  George V. Williams Feb 8 '13 at 21:31
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2 Answers

$$p(A)=\frac{\binom{10}5.\binom{15}1}{\binom{25}6}$$

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HINT: How many ways are there to choose exactly $5$ red marbles? You may choose any of the $\binom{10}5$ sets of $5$ red marbles and any of the $15$ green marbles to fill out the half dozen, so there are $15\binom{10}5$ ways to get exactly $5$ red marbles. This is the number of succesful outcomes.

  • How many (equally likely) possible outcomes are there altogether when you choose $6$ marbles from a set of $25$?

  • How do you combine these two numbers to get the probability of a successful outcome?

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