Say you ask 20 people to name their ten favourite books from a choices of 1000 books. They do not have to state the order of the favourites just simply if it is a favourite.

What is the probability of overlap?

For example that all twenty people pick 5 book in their ten that are the same? That all 20 people pick the same 6 books in their top ten,... the same X books in their top ten?

Or the probability that 6 people pick the same X books? Or that 5 people pick the same X books? Or that Y people pick the same X books?

This is a little bit like the Birthday paradox but a bit more sophisticated (I think )