Counting numbers up to 100000 with digit sum nine

How many positive integers not exceeding $100{,}000$ have decimal digits adding up to $9$? (Examples: $81$, $144$, $13212$.)

$715$. $100{,}000$ itself has digit sum 1, so pad every smaller number with leading zeros to five digits. We need non-negative solutions of $d_1+\dots+d_5=9$; no digit can exceed 9, so stars and bars gives $\binom{13}{4}=715$.