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# A Senate committee consists of 5 Republicans, 6 Democrats, and 2 Independents.

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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 three Republicans?

Darkside  Sep 7, 2018
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first off we regroup things so that we have 5 Republicans and 8 non-Republicans

this gets us

$$P[R]=\dfrac{5}{13},~P[!R] = \dfrac{8}{13}$$

now we have a simple Binomial distribution with parameters  $$n=3,~p=\dfrac{5}{13}$$

$$P[3] = \left(\dfrac{5}{13}\right)^3 = \dfrac{125}{2197}$$

Rom  Sep 7, 2018