SOLUTION: The digits 0,1,2,3,4 are to be used in a four digit ID card. How many different cards are possible if repetitions are permitted? If repetitions are not permitted?

If repetitions are permitted, then

    - you can put any of the given  5  digits to the 1-st position (5 opportunities);
    - you can put any of the given  5  digits to the 2-nd position (5 opportunities);
    - you can put any of the given  5  digits to the 3-rd position (5 opportunities);
    - you can put any of the given  5  digits to the 4-th position (5 opportunities).


In all, you have  = 625 different card ID numbers under this scenario.



If repetitions are not permitted, then another logic works:

    - you can put any of the given     5 digits to the 1-st position (5 opportunities);
    - you can put any of the remained  4 digits to the 2-nd position (4 opportunities);
    - you can put any of the remained  3 digits to the 3-rd position (3 opportunities);
    - you can put any of the remained  2 digits to the 4-th position (2 opportunities).


In all, you have 5*4*3*2 = 120 different card ID numbers under this scenario.