# Intuition behind combination problem

I came across this question on a GRE practice exam. I'm trying to build intuition behind how to correctly approach these types of problems:

A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

Initially I thought you could solve the problem by finding out 4C2 (meaning choose 2 out of 4) and then group the remaining two biographies with the novels, leaving 8 books to choose from. Then I would solve for 8C2 to find out how many ways I could select the other 2 books from the remaining 8 and multiply that with the result from 4C2. Can somebody explain why my reasoning is wrong?

Thank you.

I would count the size of the complement, i.e., compute how many selections do not satisfy the criteria. That is, count the number of selections that include 0 or 1 biographies, and then subtract that from the total number of selections, which is $\binom{10}{4}$.