Find the theoretical probability of choosing a winning 3-digit number
in the lottery.

What are the rules of the lottery?  Do you pick one number between 100
and 999?  There are 900 three digit numbers.  Or are the rules
something else?

Probably 000 to 999, in which case this the answer is very simple. 
Please review your textbook.

If we can use the same numbers over and over again, and if we can
start with zero,0, there are exactly 1000 different combinations
(including 0,0,0).

If we can again start with zero,0, but can not use the same numbers
for the other digits, then there are exactly 720 combinations.

If we can not start with zero,0, but can use it for the other digits
and can not use the same numbers again, there are exactly 648
combinations.

I hope it helps!