I've been struggling with this problem for two days. It is out of the Concepts in Probability and Stochastic Modelling textbook (1.4-13), and it goes like this:

The problem appears in one of the introductory chapters, in this case the one on combinations and permutations, but to me it seems like the problem is a bit more complex than that. For instance, when choosing the first 7 questions, the student is guessing, so the odds of him picking the right answer are:
[tex] ({\frac{2}{3}})^7 [/tex].

The sample space doesn't change as he goes about guessing the answers, so neither combinations nor permutations apply here, it seems. But then, when he fills out the remaining 8 true answers, he's no longer randomly picking answers but just marking those remaining 8 answers as false.

I am probably overthinking the problem, but at this point I'm stuck. Would greatly appreciate any help.

EDIT: crap. Didn't realize I'm not supposed to post in this forum. Apologies. Reposting in the coursework forum.