Non-negative integers means the whole numbers starting from 0. If we consider all the one-digit, two-digit and three-digit numbers at once (i.e. we allow 0 at the extreme left): The total number of numbers from 1 to 1000 : =(1 possibility for thousands place) AND (10 possibilities for hundreds place) AND (10 possibilities for tens place) AND (10 possibilities for units place) =1×10×10×10=103 The total number of numbers WITHOUT the digit 1 from 0 to 999 : =(9 possibilities for hundreds place) AND(9 possibilities for tens place) AND(9 possibilities for units place) =9×9×9=93 ∴ The number of numbers with a digit 1 will be 103−93 .