The number of all positive integers up to 500 with non-repeating digits is
Correct Answer: 378
Solution and Explanation
We need to find the number of positive integers up to 500 that have non-repeating digits.
Case 1: 1-digit numbers There are 9 possible 1-digit numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9. So, there are 9 such numbers.
Case 2: 2-digit numbers For 2-digit numbers, the first digit can be any digit from 1 to 9 (9 choices), and the second digit can be any of the remaining 9 digits (0-9, excluding the first digit). Therefore, the number of 2-digit numbers with non-repeating digits is:
9×9=81
Case 3: 3-digit numbers (up to 500) For 3-digit numbers, the first digit must be from 1 to 4 (4 choices), the second digit can be any of the remaining 9 digits, and the third digit can be any of the remaining 8 digits. Therefore, the number of 3-digit numbers with non-repeating digits is:
4×9×8=288
Total The total number of positive integers up to 500 with non-repeating digits is:
9+81+288=378
Thus, the correct answer is 378.
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