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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

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