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The number of natural numbers are their from 1 to 1000 which have none of their digits repeated, is–

Question

The number of natural numbers are their from 1 to 1000 which have none of their digits repeated, is–

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Solution

To solve this problem, we need to consider the number of digits in the numbers from 1 to 1000.

  1. For single digit numbers (1-9), there are 9 natural numbers with no repeated digits.

  2. For two-digit numbers (10-99), the first digit can be any of the 9 (1-9) and the second digit can be any of the remaining 10 digits (0-9), excluding the first digit. So, there are 9*9 = 81 such numbers.

  3. For three-digit numbers (100-999), the first digit can be any of the 9 (1-9), the second digit can be any of the remaining 10 digits (0-9), excluding the first digit, and the third digit can be any of the remaining 9 digits. So, there are 998 = 648 such numbers.

  4. For four-digit numbers (1000-9999), we only consider 1000 because it's the only four-digit number in the range 1-1000. But 1000 has the digit 0 repeated, so there are 0 such numbers.

Adding these all up, there are 9 + 81 + 648 + 0 = 738 natural numbers from 1 to 1000 which have none of their digits repeated.

This problem has been solved

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