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If repetitions of digits is not allowed, then 5! (which is 5-factorial = 5*4*3*2*1). If you assume repetition of digits is allowed, then 55.

More detail:

The math category this falls under is called combinatorix - counting the number of ways to combine things. The first answer, 5!, comes from the following reasoning:

There are 5 possibilities for the first place. Once you have chosen that places, there are four choices remaining for the next digit for each of those choices, thus giving you 5*4, and thus logic continues for the remaining digits.

For the other answer, the logic is the same, but since there is repetition allowed, each places has 5 choices.

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