Probability that one of each sex chosen.

Question

A committee consists of 8 males and 12 females. If 5 people are chosen at random to be on a subcommittee, what is the probability that at least one person from each sex is chosen?

Answer 1

This is an hypergeometric problem. The denominator is ₂₀C₅

Note _nC_{r is the binomial coefficient of pick r from n.}

The numerator is ₁₂C₅ + ₈C₅.

The probability is 1 - (numerator/denominator)

The numerator is the number of ways of picking either a committee of 5 women or of 5 men.

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