Riddles, brain puzzles and mathematical problems

[Bridge]

A teacher gives his students 10 problems and tells them that 5 of those 10 problems will be on the exam, and they will be the only questions. A student memorizes the solutions for 7 of the 10 problems. He does not know how to do any of the other 3. What is the probability the student gets at least 4 questions correct on the exam? What about scoring perfect?

Had to brush up on probability a bit before I could do this but I think I have the solution:

10C7 / 10C5 = 120 / 252 = 0.476 = 47.6%

This is the probability of the answers he memorized appearing on the exam and consequently the probability of him scoring perfect. To find out what the probability of him getting at least 4 correct on the exam is, you do the same thing but limiting the amount of questions that are chosen to 4. So, 10C7 / 10C4 = 120 / 210 = 0.571 = 57.1%