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If no digit can be repeated then there are 5 combinations, abcd, abce, abde, acde and bcde. If you regard abdc as different from abcd then each of the 5 basic sets could be arranged 24 ways and the total would be 120 combinations.
27
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.
As no digit is used twice then you have 4 choices for the first digit, but only 3 choices for the 2nd digit, 2 for the 3rd and just one for the 4th. 4 x 3 x 2 x 1 = 24 combinations.
The only combination that we can be absolutely certain makes 24 is '2' and '4'. Any others depend on exactly how you plan to combine them arithmetically.