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Assuming that leading zeros are not counted then:

The first digit can be one of {1, .. , 9} - a choice of 9.

For each of these the second can be one of the remaining 8 digits from {1, .., 9} plus the digit 0 - a choice of 9;

For each of these two choices, the third digit can be one of the 8 unchosen digits, etc.

Thus there are 9 × 9 × 8 × 7 × 6 = 27216 such numbers.

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