19. Fill in the following squares with $0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ respectively, so that the sum of the two five-digit numbers is 99999. The number of different addition equations is ( $\quad$ ). $(a+b$ and $b+a$ are considered the same equation)
【Analysis】Let $\overline{A B C D E}+\overline{\text { abcde }}=99999$
First, determine if there is a carry,
$\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}+\mathrm{E}+\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e}$
$=0+1+2+3+4+5+6+7+8+9=45=9+9+9+9+9$, no carry.
(You can also determine no carry by $8+9=17$, which cannot be 19)
Next, form five pairs of 9: $9=0+9=1+8=2+7=3+6=4+5$
$\mathrm{a}+\mathrm{b}$ and $\mathrm{b}+\mathrm{a}$ are considered the same, so let 0 be in $\mathrm{ABCDE}$,
The different permutations of $\mathrm{ABCDE}$ are $2 \times 2 \times 2 \times 2 \times 4 \times 24=1536$ (ways).
When $\overline{A B C D E}$ is fixed, it uniquely determines $\overline{\text { abcde }}$.
There are a total of 1536 ways to fill in.