Find the number of natural numbers from 1 to 1000 having none of their digits repeated.

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730

738

740

749

answer is B.

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Detailed Solution

There can be 3 kinds of numbers: 1 digit, 2 digit, 3 digit numbers.
No. of 1 digit no.s is 9 obviously.
No. of 2 digit no.s is 9×9 = 81 as the 1st digit can't be 0 but the 2nd digit can
Similarly no. of 3 digit no.s = 9×9×8 = 648
Total no. of no.s = 738
Hence option (2) is correct.

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