Calculate the number of combinations of a sequence of numbers in a particular order
Can you solve the problem for $n=1$?
Can you deduce the answer for $k+1$, if you know the answer for $k$? 
(hint: you need an $n\times 10$ table, the $k$-th row devoted for problem size $k$, the columns for partial answers...)

ps: I think that the answer is $9+0+1+1+2+1+3+1+3+2=23$ for n=2 (and 125 for $n=3$)

0: 10,...,90
1: - 
2: 22
3: 33
4: 24,44
5: 55
6: 26,36,66
7: 77
8: 28,48,88
9: 39,99