How many different 4-digit personal identification numbers are possible if no digit can be used twice?

A PIN can begin with 0, so there are 10 choices for the first digit. With no digit repeated, there are then 9 choices for the second, 8 for the third, and 7 for the fourth. Multiplying gives 10 × 9 × 8 × 7 = 5,040, so the correct choice is 5,040.

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