On a six-question multiple-choice test there are five possible answers for each question, of which one is correct (C) and four are incorrect (I). If a student guesses randomly and independently, find the probability of

a. Being correct only on questions 1 and 4 (i.e., scoring C, I, I, C, I, I).

b. Being correct on exactly two questions.

c. If X equals the number of correct answers in the six guesses, what is the p.m.f.; the mean; and the variance of X?