Assignment:
A group of high school students is preparing to compete with groups from other schools on a TV show in which questions about various academic subjects are asked of the contestants. There are seven boys and five girls in the group. Every time this school is represented on the show, a team of three students participates. How many different teams (combinations of three students) can be formed from this group if every team includes at least one boy and at least one girl? (Two teams are considered to be different if they differ in at least one member.)
Provide complete and step by step solution for the question and show calculations and use formulas.