Multiple-choice questions each have four possible answers ( $a, b, c, d)$, one of which is correct. Assume that you guess the answers to three such questions. a. Use the multiplication rule to find $\mathrm{P}(W \mathrm{CC})$, where $\mathrm{C}$ denotes a correct answer and $W$ denotes a wrong answer. $P(W C C)=\square$ (Type an exact answer.) b. Beginning with WCC, make a complete list of the different possible arrangements of two correct answers and one wrong answer, then find the probability for each entry in the list. \[ \begin{array}{l} P(W C C) \text { - see above } \\ P(C C W)=\square \\ P(C W C)=\square \end{array} \] (Type exact answers.) c. Based on the preceding results, what is the probability of getting exactly two correct answers when three guesses are made? (Type an exact answer.)

Step 1 ：Define the probability of guessing a correct answer (C) as \(P_C = 0.25\) and the probability of guessing a wrong answer (W) as \(P_W = 0.75\).

Step 2 ：Use the multiplication rule of probability to find the probability of the sequence WCC. The multiplication rule states that the probability of two independent events occurring is the product of their individual probabilities. Therefore, \(P_{WCC} = P_W \times P_C \times P_C = 0.75 \times 0.25 \times 0.25 = 0.046875\).

Step 3 ：Similarly, find the probabilities of the sequences CCW and CWC. Since the events are independent, these probabilities are the same as for WCC. Therefore, \(P_{CCW} = P_C \times P_C \times P_W = 0.25 \times 0.25 \times 0.75 = 0.046875\) and \(P_{CWC} = P_C \times P_W \times P_C = 0.25 \times 0.75 \times 0.25 = 0.046875\).

Step 4 ：Final Answer: The probability of the sequence WCC is \(\boxed{0.046875}\), the probability of the sequence CCW is \(\boxed{0.046875}\), and the probability of the sequence CWC is \(\boxed{0.046875}\).