How many positive whole numbers less than 10,000 have digits adding up to 9?

Write each number with 4 digits (leading zeros allowed). We need $a+b+c+d=9$ with digits 0–9: ${}^{12}{C}_3=220$. No digit can exceed 9, and 0000 is not counted since its sum is 0. (165 $={}^{11}{C}_3$ counts only up to 999.)