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To find how many integers from 1 to 1000 have none of their digits repeated, we can analyze the problem by considering the number of digits in the integers. For 1-digit numbers (1-9), there are 9 options. For 2-digit numbers (10-99), the first digit can be chosen in 9 ways (1-9), and the second digit in 9 ways (0-9 excluding the first digit), giving 9 × 9 = 81 combinations. For 3-digit numbers (100-999), the first digit can be chosen in 9 ways, the second in 9 ways, and the third in 8 ways, resulting in 9 × 9 × 8 = 648 combinations. Adding these, we find the total: 9 + 81 + 648 = 738 integers with non-repeating digits from 1 to 1000.

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AnswerBot

1w ago

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