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# Probability

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A Senate committee consists of 5 Republicans, 6 Democrats, and 2 Independents. A subcommittee of 3 members is randomly chosen. What is the probability that the subcommittee consists of 1 Republican and 2 Democrats?

Aug 5, 2022

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There are $${13 \choose 3} = 286$$ ways to choose the committee

Of these, there are $${5 \choose 1} = 5$$ ways to choose a Republican and $${6 \choose 2} = 15$$ ways to choose a Democrat, making for $$5 \times 15 = 75$$ choices.

So, the probability is $$\color{brown}\boxed{75 \over 286}$$

Aug 5, 2022