11. (12 points) If a three-digit number $\overline{\mathrm{abc}}$ (where $a, b, c$ are all non-zero digits) satisfies $\overline{\mathrm{ab}}>\overline{\mathrm{bc}}>\overline{\mathrm{ca}}$, then the three-digit number is called a “Longteng number”. How many “Longteng numbers” are there?
【Solution】Solution: According to the analysis, $\overline{\mathrm{ab}}>\overline{\mathrm{bc}}>\overline{\mathrm{ca}}$, then $a \geqslant b \geqslant c$, divided into three cases:
(1) When $a=b>c$, there are $C_{9}^{2}=36$;
(2) When $a>b=c$, from $\overline{\mathrm{bc}}>\overline{c a}$ we know, $c>a$ which contradicts the problem, so it does not hold;
(3) When $a>b>c$, $a, b, c$ can take unequal numbers between $1 \sim 9$, there are $C_{9}^{3}=84$.

In summary, there are: $36+84=120$ "Longteng numbers".
Therefore, the answer is: 120.