7. Prove by mathematical induction that for each $n \ge 3$, if $A = \{1, \dots, n\}$ then the number of sets of the form $\{i, j, k\}$, where $1 \le i < j < k \le n$, is $\frac{n(n-1)(n-2)}{6}$.
In this problem, you are allowed to use the fact that A has $\frac{n(n-1)}{2}$ subsets of the form $\{i, j\}$ with $1 \le i < j \le n$.