The number of all natural numbers up to 1000 with non-repeating digits is
- 648
- 585
- 504
- 738
The Correct Option is D
Approach Solution - 1
The correct option is (D): 738
Approach Solution -2
1. For 1-digit numbers: There are 9 one-digit numbers (from 1 to 9).
2. For 2-digit numbers:
- For the tens place, any digit from 1 to 9 can be chosen (excluding 0).
- For the units place, any digit can be chosen.
- So, there are \(9 \times 9 = 81\) possibilities.
3. For 3-digit numbers:
- For the hundreds place, any digit from 1 to 9 can be chosen.
- For the tens place, any digit can be chosen (excluding the digit already used in the hundreds place).
- For the units place, any remaining digit can be chosen.
- So, there are \(9 \times 9 \times 8 = 648\) possibilities.
Therefore, the total number of natural numbers up to 1000 with non-repeating digits is:
\[9 + 81 + 648 = 738\]
Thank you for the clarification. The correct answer is indeed \(\boxed{738}\).
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