$28 \cdot 31$ Using the digits $1,2,3,4,5,6,7,8$ to form two four-digit numbers, to make the product of these two four-digit numbers as large as possible, the larger one of them is
(A) 8765 .
(B) 8642 .
(C) 8531 .
(D) 8672 .
(China Zhejiang Ningbo Junior High School Mathematics Competition, 1985)
［Solution］First, we prove the following fact:
If $a>b, \quad c>d(a, b, c, d \in N)$, then $\overline{a d} \cdot \overline{b c}>\overline{a c} \cdot \overline{b d}$.
Notice that $\overline{a d} \cdot \overline{b c}-\overline{a c} \cdot \overline{b d}$
$$
\begin{array}{l}
=(10 a+d)(10 b+c)-(10 a+c)(10 b+d) \\
=10(a-b)(c-d)>0
\end{array}
$$

This completes the proof.
When dividing $1 \sim 8$ into two groups, 8 and 7 should be the leading digits; when placing 6 and 5, they should be paired as 85 and 76;
When placing 4 and 3, they can be paired as 853 and 764; the final grouping is 8531 and 7642. Therefore, the answer is $(C)$.