Get a random file from a random folder

I have a folder "testfiles" in my project directory, which contains a lot of others folders. Those folders all have names like "alice-g" (firstname and then first letter from lastname). Each of those folders contains some other folders, not always the same number. And in each of those last folders, i got a bunch of files, all named with number ("1.", "2.", "3." and so on).

What i want to do is going into this "testfiles" directory, randomly select a folder, get his name, then randomly select another folder in it and finally select a random file in this folder (and get his name).

I have found this post which say we can pick a random file from a folder this way:

File[] files = dir.listFiles();
Random rand = new Random();
File file = files[rand.nextInt(files.length)];

This sound clear and easy to me. However, since all my files have "easy numbered names", i wonder if there is a way to do this without making list of all files (i can have thousand of files in a directory, dunno how efficient this will be then...). Is there any way to just get the number of files in a directory (without making this list of all files)? Then i will just have to select a random number between 1 and the amount of files and i can set the filename and select the file.

Second, this solve the problem of selecting a random file, but not of selecting a random directory (and get his name).

It may be important to say that i'm on Ubuntu 16.04? I've never worked with directories in java, so dunno if it's really relevant.