a. The probability that all 4 members on the committee will be girls is (Type an integer or a simplified fraction.)
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If we're considering a committee made up of girls and boys, the probability of all members being girls depends on the total number of girls and boys available for selection. For example, if there are 6 girls and 4 boys, the total number of committee options would be \( \binom{10}{4} \), while the ways to choose 4 girls would be \( \binom{6}{4} \). To calculate the probability, you’d divide the combinations of choosing only girls by the total combinations available. Want to spice it up? Let’s say your middle school had a committee with 15 girls and 5 boys! The probability of selecting an all-girls committee would be the ratio of the ways to choose 4 girls to choosing any 4 members. With this scenario, it actually turns out to be a pretty sweet probability—just calculate \( \frac{\binom{15}{4}}{\binom{20}{4}} \) and you'll impress your friends with some math magic!