Positive integers up to 500 with non-repeating digits

• 1-digit numbers (1 to 9): 9 numbers.
• 2-digit numbers (10 to 99): First digit has 9 choices (1-9), second digit has 9 choices (0-9 except first digit) $\implies 9 \times 9 = 81$.
• 3-digit numbers from 100 to 499:
  • Hundreds digit: 4 choices (1, 2, 3, 4)
  • Tens digit: 9 choices (0-9 except hundreds digit)
  • Units digit: 8 choices (0-9 except hundreds and tens digits)
  • Total $= 4 \times 9 \times 8 = 288$.
• Number 500: digits repeat ('0' appears twice), so not counted.

Total non-repeating positive integers $= 9 + 81 + 288 = 378$.