How do I create a database that will generate a quiz with so many questions from each group?

This question cannot be easily answered. A database cannot do this on its own--you need use a programming language as the medium that interacts with the user and the database. If you have a more specific question, we could probably answer it. But, there's no way to really answer your current question.

The specification is a bit soft. You might begin with a table along the lines

create table questions (

category integer references categories.id,

question character varying(200),

answer character varying(200)

);

To then randomly select 10 questions from category 4 you do something like:

select *, random() from questions where category = 4 order by random() limit 10;

To add questions from the other categories simply repeat the query for each.

Youtube.