Three, Multiple Choice Questions (12 points each, total 48 points)
12. (12 points) In the program "Where Are We Going, Dad?", there is a task where five children participating in the task (Tian Tian, Shitou, Kimi, Cindy, Angela) need to switch dads (each child can choose any one of the other four fathers except their own). How many different outcomes are there for the final choices of the five children?
A. 40
B. 44
C. 48
D. 52
【Solution】Solution: Let the five fathers be $A, B, C, D, E$, and the five children be $a, b, c, d, e$. $a$ has 4 choices. Assume $a$ chooses $B$, then let $b$ choose, with two possibilities: choosing $A$ and not choosing $A$,
(1) Choosing $A$, $c, d, e$ choose three people to derange,
(2) Not choosing $A$, then $b, c, d, e$ choose as in the derangement of 4 people. Therefore, $S_{5}=4\left(S_{4}+S_{3}\right)$.

Similarly, $S_{4}=3\left(S_{3}+S_{2}\right), S_{3}=2\left(S_{2}+S_{1}\right)$,
and $S_{1}=0$ (impossible to derange), $S_{2}=0$, so $S_{3}=2, S_{4}=9, S_{5}=44$,
Therefore, the answer is: $B$.