Example 3: Five teachers, A, B, C, D, and E, predict the rankings of five students, A, B, C, D, and E, in a competition:
Teacher A predicts: B 3rd, C 5th;
Teacher B predicts: E 4th, D 5th;
Teacher C predicts: A 1st, E 4th;
Teacher D predicts: C 1st, B 2nd;
Teacher E predicts: A 3rd, D 4th.
The competition results show that each rank was correctly predicted by someone. Determine the rankings of each student.
Explanation: Fill in the guesses of the 5 teachers in Table 1.
Table 1
\begin{tabular}{|c|c|c|c|c|c|}
\hline Rank & 1 & 2 & 3 & 4 & 5 \\
\hline Jia & & & $B$ & & $C$ \\
\hline Yi & & & & $E$ & $D$ \\
\hline Bing & $A$ & & & $E$ & \\
\hline Ding & $C$ & $B$ & & & \\
\hline Wu & & & $A$ & $D$ & \\
\hline
\end{tabular}

The competition results show that each rank was guessed correctly by someone, and the 2nd rank was only guessed correctly by Ding, so the 2nd rank must be $B$. Therefore, $B$ cannot be the 3rd rank, so the 3rd rank can only be $A$. Similarly, the 1st rank is $C$, the 5th rank is $D$, and the 4th rank is $E$.

Note: By organizing the originally disordered information into a table, the problem becomes clearer, which is an effective method for solving more complex logical reasoning problems.