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# If a committee of six students is chosen at random from a group of six boys and four girls, what is the probability that the committee conta

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If a committee of six students is chosen at random from a group of six boys and four girls, what is the probability that the committee contains the same number of boys and girls? Express your answer as a common fraction.

May 19, 2021

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Number of ways for the committee to have 3 boys, 3 girls: $$\binom{6}{3} \cdot \binom{4}{3} = 20 \cdot 4 = 80.$$

Number of total ways: $$\binom{10}{6} = 210$$

So, the answer is $$\frac{8}{21}.$$

May 19, 2021
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Thanks !

mathisopandcool  May 19, 2021