2006 AMC 10A Problems/Problem 21
Since we are asked for the number of positive 4-digit integers with at least 2 or 3 in it, we can find this by finding the total number of 4-digit integers and subtracting off those which do not have any 2s or 3s as digits.
The total number of 4-digit integers is , since we have 10 choices for each digit except the first (which can't be 0).
Similarly, the total number of 4-digit integers without any 2 or 3 is .
Therefore, the total number of positive 4-digit integers that have at least one 2 or 3 in their decimal representation is