We need to find how many positive integers up to 500 have unique digits (no repeating digits).
Case 1: 1-digit numbers There are 9 possible 1-digit numbers (1 through 9). Thus, there are 9 such numbers.
Case 2: 2-digit numbers For 2-digit numbers, there are 9 choices for the first digit (1-9). The second digit can be any of the remaining 9 digits (0-9, excluding the first digit). The total number of 2-digit numbers with unique digits is:
9 × 9 = 81
Case 3: 3-digit numbers (up to 500) For 3-digit numbers up to 500, the first digit has 4 choices (1-4). The second digit has 9 choices (any digit except the first). The third digit has 8 choices (any digit except the first two). The total number of 3-digit numbers up to 500 with unique digits is:
4 × 9 × 8 = 288
Total The total number of positive integers up to 500 with unique digits is:
9 + 81 + 288 = 378
Therefore, the answer is 378.