12. (5 points) Before New Year's Day, Xiaofang made greeting cards for her five classmates. When putting the cards into envelopes, she made a mistake, and none of the five classmates received the card Xiaofang made for them; instead, they received cards Xiaofang made for others. In total, there are $\qquad$ possible scenarios.
【Analysis】(1) When all five greeting cards are given incorrectly, and there are no mutual wrongs between any two, then student No. 1 has four wrong ways. For example, if student No. 1 gets card No. 2, then student No. 2 cannot get card No. 1 or card No. 2, leaving only 3 wrong ways. Student No. 3, besides not getting card No. 3, also cannot get the cards already received by students No. 1 and No. 2, leaving only 2 scenarios. Therefore, there are: $4 \times 3 \times 2 \times 1=24$ ways; (2) When all five greeting cards are given incorrectly, and there are mutual wrongs between some pairs, then the remaining three cards must also be mutually wrong. When a pair of mutually wrong students is determined, the remaining 3 students can only be mutually wrong in 2 ways. Selecting 2 students from 5, there are 10 ways to choose; $2 \times 10=20$ ways; Therefore, there are a total of: $24+20=44$ ways.

【Solution】According to the analysis, the total number of ways for both scenarios is:
$$
\begin{array}{l}
4 \times 3 \times 2 \times 1+5 \times 4 \div 2 \times 2, \\
=24+20, \\
=44 \text { (ways); }
\end{array}
$$

Answer: There are a total of 44 possible scenarios.
The answer is: 44.