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# math problem

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We know there are 100 members and currently there are 48 Democrats and 52 Republicans. Use this information to answer the following. Step 1 of 5: What is the probability that a random committee of 6 will contain all Democrats?

Feb 24, 2019

$$\text{The number of Democrats selected out of 6 is a random variable having a binomial distribution}\\ \text{with parameters }n=6,~p = \dfrac{48}{100}=\dfrac{12}{25}\\ p[6] = \dbinom{6}{6} p^6 = \left(\dfrac{12}{25}\right)^6 = \dfrac{2985984}{244140625} \approx 0.01223$$