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# probability

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Jamal's friends toss 12 balls to him at the same time. Three balls are red, 3 are green, 3 are blue, and 3 are white. Jamal manages to catch 5 of the balls.What is the probability that he catches 2 red balls and 1 ball of each of the other colors?

Feb 24, 2021

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There are $\binom{12}{5}$ ways to choose all the balls.

There are $\binom{3}{2}$ ways to catch the red ball, and $\binom{3}{1}$ ways to catch each of the other ones.

The answer is $\frac{\binom{3}{2}\left(\binom{3}{1}\right)^3}{\binom{12}{5}}=\frac{81}{792}=\boxed{\frac{9}{88}}$.

Feb 24, 2021