How many $3$-digit numbers have a digit sum of $21$? I have the following question:

How many $3$-digit numbers have a digit sum of $21$?

I can count it by taking separate cases of three digit numbers such that their digit sum is $21$ & by calculating all possible numbers that can be made from each case and by adding them to get the result.
My question: Is there any direct combination formula to calculate this?
(I don't think stars and bars method works here)

Here is a solution using generating functions: The solution to this problem is equal to the coefficient of $x^{21}$ in the expansion of
$$(1 + x + x^2 + \cdots + x^9)^{2}(x + x^2 + x^3 + \cdots + x^{9}),$$
which Wolfram Alpha says to be $28$.
