3. Let the set $E=\left\{a_{1}, a_{2}, \cdots, a_{10}\right\}$ have five-element subsets such that: any two elements of $E$ appear in at most two subsets. The maximum number of such five-element subsets is ( ).
A. 252
B. 10
C. 8
D. 18
3. C.

Let the number of 5-element subsets that satisfy the condition be $n$. Each element in $E$ appears no more than 4 times, so we have $5n \leqslant 10 \times 4$, which gives $n \leqslant 8$. The construction is as follows:
$$
\begin{array}{l}
\left\{a_{1}, a_{2}, a_{3}, a_{4}, a_{5}\right\},\left\{a_{1}, a_{6}, a_{7}, a_{8}, a_{9}\right\},\left\{a_{1}, a_{3}, a_{5}, a_{6}, a_{8}\right\},\left\{a_{1}, a_{2}, a_{4}, a_{7}, a_{9}\right\}, \\
\left\{a_{2}, a_{3}, a_{6}, a_{7}, a_{10}\right\},\left\{a_{3}, a_{4}, a_{7}, a_{8}, a_{10}\right\},\left\{a_{4}, a_{5}, a_{8}, a_{9}, a_{10}\right\},\left\{a_{2}, a_{5}, a_{6}, a_{9}, a_{10}\right\} .
\end{array}
$$