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The first digit can be any one of the ten symbols, 0 thru 9. For each of those . . .

The second digit can be any one of the 9 that weren't used in the first place. For each of those . . .

The third digit can be any one of the 8 that you haven't used yet. For each of those . . .

The fourth digit can be any one of the 7 that haven't been used yet.

Total number of possible arrangements = (10 x 9 x 8 x 7) = 5,040

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Q: How many different four digit combinations are there of the numbers zero through nine without using the same number twice in each combination?
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