A fair six-sided die is thrown twice and a fair coin is tossed thrice. All five trials are independent, and the order of occurrence is recorded.
Answer the following questions:
a. (i) Determine the total number of possible ordered outcomes.
b. (ii) Compute the probability that exactly one of the two throws of the die shows a 6 and exactly two of the three tosses of the coin show heads.
c. (iii) Compute the probability that the sum of the numbers obtained on the two dice is greater than 8 and at least two heads appear in the three coin tosses.
d. (iv) Compute the probability that at least one of the events described in parts (ii) or (iii) occurs.