Question 95
A class has $n$ students. Every day class teacher chooses 3 students to form a team to study together. Each student works in a team with every other student not more than once. If $k$ is the number of maximum possible days then prove the inequality
$$
\frac{n(n-3)}{6} \le k \le \frac{n(n-1)}{6} \text{ holds.}
$$
$$
\frac{n(n-3)}{6} \le k \le \frac{n(n-1)}{6} \text{ holds.}
$$