Hello there. To solve this question, we have to remember some properties about combinatorics.
We want to determine how many passwords can be created using 3 lowercase letters and 1 numeric digit if letters can be used more than once.
For this, remember the alphabet has 26 letters, from a to z.
As all the letters are lowercase, we won't have to deal with combinations of lowercase and uppercase letters (that would be considered different even though they are the same).
We only have 10 numeric digits as well, from 0 to 9.
Therefore, by the multiplicative principle, the number of passwords is given by
[tex]26\cdot26\cdot26\cdot10=175760[/tex]
This is the answer to this question and it is contained in the first option.
