Explanation:

For a number to be greater than zero it must have at least a single non zero digit and for a number to be less than a million it can have a maximum of 6 digits.

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Now you have 6 places to fill, each of which can be filled with 3 digits (0,7,8).

So you can have 3*3*3*3*3*3 = 3^6 numbers, but in these numbers, one number will contain all the digits zero.

So final answer is (3^6) -1 = 729 -1 = 728