Example 2-55 In the permutations of the numbers $1,2,3, \cdots, 9$, find the number of derangements where even numbers are in their original positions, and the rest are not in their original positions.
Actually, it is the derangement problem of the 5 numbers $1,3,5,7,9$, the total number is
$$
\begin{aligned}
& 5!-C(5,1) 4!+C(5,2) 3!-C(5,3) 2!+C(5,4) 1!-C(5,5) \\
= & 120\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{24}-\frac{1}{120}\right)=60-20+5-1=44
\end{aligned}
$$