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The question is incorrect since there are 210 - 1 possible combinations.

The digit 0 can be in the combination or out. That gives 2 ways.

With each, the digit 1 can be in the combination or out - 2*2 = 22 ways.

With each, the digit 2 can be in the combination or out = 23 ways.

With each, the digit 3 can be in the combination or out = 24 ways.

etc.

So 210 ways in all except that one of them is the null combination.

Now 210 = 1024 so there are only 1023 combinations.

If, instead, you allow the digits to be used many times, there is no limit to the number of combinations.

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14y ago

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