How many 4-digit numbers are there, when a digit may be repeated any number of times?
The available digits are: $\; 0, \; 1, \; 2, \; 3, \; 4, \; 5, \; 6, \; 7, \; 8, \; 9$
$\therefore \;$ Number of available digits $= 10$
The thousand's place can be selected from the digits $\; 1, \; 2, \cdots , 9 \;$ in $\; 9$ ways
The hundred's place can be selected from the digits $\; 0, \; 1, \; 2, \cdots, 9 \;$ in $\; 10$ ways
The ten's place can be selected from the digits $\; 0, \; 1, \; 2, \cdots, 9 \;$ in $\; 10$ ways
The unit's place can be selected from the digits $\; 0, \; 1, \; 2, \cdots, 9 \;$ in $\; 10$ ways
$\therefore \;$ Number of possible 4-digit numbers $= 9 \times 10 \times 10 \times 10 = 9000$