Question

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?

Answer 1

The first digit can be any of 9.
The second digit can be any of the remaining 8.
The third digit can be any of the remaining 7.
The fourth digit can be any of the remaining 6.
The final digit can be any of the remaining 5.

The number of possible ID numbers is 9·8·7·6·5 = 15,120.