The entire space consists of all possible combinations of choosing three questions out of 100. There are however, 90C3 and 90C2*10 possible combinations that will allow him to pass the test so:

Total # of possible 3-question combinations: 100 choose 3

Total # of possible 3-question combinations that student knows all answers: 90C3

Total # of possible 3-question combinations that students knows two answers and doesn't know the last one: (90 choose 2)X10

Probability he will be given a 3-question combinaiton he knows:

This assumes that the test is premade, and its simply a matter of selecting one of the premade tests. If he is actually picking questions then its much easier: