8. For any non-empty finite set $A$ of real numbers, let $s(A)$ be the sum of the elements in $A$. There are exactly 613 -element subsets $A$ of $\{1, \ldots, 23\}$ with $s(A)=36$. Find the number of 3 -element subsets of $\{1, \ldots, 23\}$ with $s(A)<36$.
8. Ans: 855

The map $\{a, b, c\} \rightarrow\{24-a, 24-b, 24-c\}$ is a bijection from the set of 3-element subsets of $\{1, \ldots, 23\}$ with $s(A)36$. The number of 3 -element subsets of $\{1, \ldots, 23\}$ is $\binom{23}{3}=1771$. Therefore, the number of 3-element subsets of $\{1, \ldots, 23\}$ with $s(A)<36$ is
$$
\frac{1}{2}[1771-\text { number of } 3 \text {-element subsets of }\{1, \ldots, 23\} \text { with } s(A)=36]=855 \text {. }
$$