A University exam consists of n multiple choice questions. For the first question there are k1 possible answers, and for the second one there are k2 answers and so on, and finally for the nth question there are kn answers to choose from.

(i) If a student does not know the answer to any question and chooses her answers completely at random, how many different selections she has in total? What is the probability that she answers all questions correctly?

(ii) Assuming again that the student gives her answers at random, what is the probability that she does not answer any questions correctly?