Hi Edward,

You have 10 choices for the digit in the first row and once you have chosen it you have 9 digits to choose from for the second row. Once these two are chosen you have 8 choices for the third row and so on. Since you have 4 rows there are $10 \times 9 \times 8 \times 7 = 5040$ possible codes.

To list them you can use a tool on the Math Is Fun site. Set n = 10, r = 4, toggle is repetition allowed? to no and you will get 5040 as the number of permutations. To obtain a list, in the List Them box type 0 to 9, separated by commas and select list.

Good luck in getting it open,
Penny