A state university issues five-digit student identification numbers to all of its students. None of the identification numbers contain the digit 0 and the digits cannot be repeated. How many ways are there to arrange five digits if only the numerals 1 through 9 are used?

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Asked and answered elsewhere.
https://brainly.com/question/10614810

The number of permutations of nine numbers taken 5 at a time is ...
P(9, 5) = 15,120