7.2. In 7a grade, there are 33 students. At the beginning of the school year, two clubs were organized in the class. According to school rules, a club can be organized if at least $70 \%$ of all students in the class sign up for it. What is the smallest number of students who could have signed up for both clubs simultaneously?
Answer: 15 students. Solution. In each club, there should be no less than $33 \cdot 0.7=23.1$ people, which means no less than 24 people. Let $n_{1}, n_{2}$ be the number of students who signed up for the first and second club, respectively, and $n$ be the number of students who signed up for at least one club. Obviously, $n \leq 33$ (note that it is not necessarily $n=33$, as the problem does not state that every student signed up for a club). Then the number of students who signed up for both clubs is $n_{1}+n_{2}-n$, since in the sum $n_{1}+n_{2}$, those who signed up for both clubs are counted twice. Therefore, $n_{1}+n_{2}-n \geq 24+24-33=15$, and this number is achieved when 9 people signed up for only one club and 15 people signed up for both clubs.