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Question 65
The number of all natural numbers up to 1000 with non-repeating digits is
Solution
1-digit numbers => We have 1 to 9 => 9
2-digit numbers => x y, we have 9 ways to choose x from 1 to 9 => 9 ways and 9 ways to choose y (0 to 9 except x) => 9*9 = 81
3-digit numbers => x y z, we have 9 ways to choose x, 9 ways to choose y and 8 ways to choose z => 9*9*8 = 648.
Total numbers till 1000 without digits repeated in them is 9 + 81 + 648 = 738.
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