A College Has Seven Applicants for Three Scholarships: Four Females

Short Answer

A college has seven applicants for three scholarships: four females and three males. Suppose that the seven applicants are equally qualified and that no preference is given by the selection committee for choosing either gender. Let x equal the number of female students chosen for the three scholarships.
What is the mean of the distribution of x?
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What is the variance of the distribution of x?
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What is the probability that only one female will receive a scholarship?
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What is the probability that two females will receive a scholarship?
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What is the probability that none of the three males will receive a scholarship?
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What is the probability that none of the four females will receive a scholarship?
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