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a. For each of the following statements, say whether it is true or false. i. There are in total 10 P(9, 4) possible different number plates consisting of 6 digits (0 to 9) with exactly 2 of the same digit. ii. Three standard (6-sided) dice are rolled. One is red, one is blue, and one is green. If the particular number showing on each coloured die is important, then there are in total 6^3 possible different outcomes. iii. A bag contains 10 black and 12 white balls and each ball is considered distinguishable from each other. There are in total C(10, 5)C(12, 3)C(10, 6)C(12, 2) different ways to select 8 balls so that exactly 5 or 6 are black. iv. Two 6-sided fair dice are rolled. The probability that at least one of the dice is 6, is 1/3 . v. Tossing a fair coin and getting a head is mutually exclusive from rolling a 6-sided die and getting a 5. b. A necklace is to be formed by threading 8 beads on a circle of string. The beads are taken from a bag containing 14 different beads. How many options are there for a necklace if the knot holding the string together is not visible? Explain your answer. [5 Marks] c. An insurance company issues car insurance, homeowner insurance, and life insurance. Of the claims the company pays, 50% are car, 40% are homeowner, and 10% are life. The company is primarily concerned with claims over RM50, 000 that it pays. History has shown that 10% of car claims, 30% of homeowner claims, and 90% of life insurance claims exceed RM50, 000. i. What percentage of claims paid by this company exceed RM50, 000? [12 Marks] ii. Given that this company pays a cliam over RM50, 000, what is the probability that it is a homeowner claim?