Integers below a million with digit sum 19

Count the positive integers less than $1{,}000{,}000$ whose decimal digits add up to $19$.

$30492=\binom{24}{5}-6\binom{14}{5}$. Pad to six digits $d_1+\dots+d_6=19$ with $0\le d_i\le 9$. Stars and bars gives $\binom{24}{5}$ without the cap; a digit exceeding $9$ can happen for only one digit at a time (two would need $20$), and each such case leaves $\binom{14}{5}$ solutions, so subtract $6\binom{14}{5}$.