How many 4-digit numbers have digits that add up to 10?

Let the first digit be $a\ge 1$; write $a=a^{\prime }+1:a^{\prime }+b+c+d=9$ has ${}^{12}{C}_3=220$ non-negative solutions. Only $a^{\prime }=9$ (first digit 10) breaks the digit limit; no other digit can exceed 9. So $220-1=219$.