Quick question on probablility

Here is the problem:

A student prepares for an exam by studying a list of ten problems.

She can solve six of them. For the exam, the instructor selects five problems at random from the ten on the list given to the students. What is the probability that the student can solve all five problems on the exam?

Here is how I solved it:

I found all possible exams which is (10 choose 5) = 252

then to find the probability I calculated all possible subsets with 5 questions she can solve and got (6 choose 5) = 6

So P(a)= 6/252 = 0.0238 ? roughly 2.38%?

What am I doing wrong here, some one said that I have to use binomial probability theorem here but it can't be because that is a few chapters away in the book, there has to be a way of solving it without it... Please help