Another possibility is that the implementation of the count down latch is just an example for the interview.... meaning even if you memorized the implementation, it will likely not be enough.
In an interview, personally, I would like to see the candidate understand the basics. How to share data? How to protect the data? How threads sends notifications to each other, in order to share data more efficiently... And a discussion regarding the possible implementation of a count down latch, where the shared data is a "release flag", and triggers the
thread(s) behavior (group waking up) works well.
Or in other words, after you give an simple implementation overview, I would expect lots of followup questions too.
Henry