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, 1 Democrat, and 1 Independent?
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<|im_start|>user
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, 1 Democrat, and 1 Independent?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\dfrac{30}{143}
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, 1 Democrat, and 1 Independent?
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