Final answer:
In mathematics, high school students can determine the number of possible committees with specific gender compositions using the combination formula.
Explanation:
a. To calculate the number of 7-member committees with 3 boys and 4 girls, use the combination formula. There are 7 ways to choose 3 boys from 7 and 7 ways to choose 4 girls from 7, resulting in 7C3 * 7C4 committees.
b. For committees with at least one member of each sex, calculate the total number of committees (7-member) minus the ones without both sexes, i.e., committees with all boys or all girls.
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