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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, 1 Democrat, and 1 Independent?

Guest Oct 11, 2018

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This is a multivariate hypergeometric distribution.

$P[\{R,D,I\}] = \dfrac{\dbinom{5}{1}\dbinom{6}{1}\dbinom{2}{1}}{\dbinom{13}{3}}=\dfrac{30}{143}$

Rom Oct 11, 2018

edited by Rom Oct 11, 2018
edited by Rom Oct 11, 2018

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Rom · Answer 1 · 2018-10-11T05:57:29

This is a multivariate hypergeometric distribution.

$P[\{R,D,I\}] = \dfrac{\dbinom{5}{1}\dbinom{6}{1}\dbinom{2}{1}}{\dbinom{13}{3}}=\dfrac{30}{143}$

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