count of numbers between A and B (inclusive) that have sum of digits equal to S
GolfScript, 35 bytes

~:S;),&gt;{.10base{+}*S=!{;}*}%(\,)]n*


How it works

~         # Interpret the input string.
:S;       # Save the last integer in variable “S” and pop it from the stack.
),        # Increment it by 1 and create the array “[0 ... B]”
&gt;         # Remove the first “A” elements. This leaves the array “[A ... B]”
{         # For each of those integers:
  .10base # Push its digits in base 10.
  {+}*    # Add the digits.
  S=!{;}* # If the sum is not equal to “S”, pop the integer from the stack.
}%        # Collect the results into an array.
(\        # Extract the first and swap it below the array.
,)        # Count the elements of the array of all remaining integers and increment by one. 
n\        # Separate the results by a newline.