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)

$$a+b+c=21\implies(9-a)+(9-b)+(9-c)=6$$
Apply stars and bars to $x+y+z=6$ to get $\binom{8}{2}=28$ solutions.
