2006 AMC 10A Problems/Problem 21
Problem
How many four-digit positive integers have at least one digit that is a 2 or a 3?
Solution
Since we are asked for the number of positive 4-digit integers with AT LEAST ONE 2 or 3 in it, we can find this by finding the number of 4-digit + integers that DO NOT contain any 2 or 3.
Total # of 4-digit integers: 
Total # of 4-digit integers w/o 2 or 3: 
Therefore, the total number of positive 4-digit integers that have at least one 2 or 3 in it equals: 9000-3584=5416 (E)
