Probability that the student can solve 5 of 7 problems on the exam

A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?

I am really confused by this problem. My first initial thought was to do:

(5 chose 7)(7 chose 0)/ (12 chose 7)

• I believe it should be (7 chose 5)(7 choose 2)/ (12 chose 7) is this correct? – user125627 Feb 13 '14 at 19:24

In order for the student to solve exactly $5$ problems out of the $7$, the exam must contain exactly $5$ out of the $7$ problems the student knows how to solve, and exactly $2$ of the other three problems.
• @user125627 Is the student gets exactly $5$ of $7$ questions right, what does he do on the other two? – N. S. Feb 14 '14 at 2:24