d) A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j for j = 1, 2, 3, 4, 5, 6. In 6 independent throws of this die, what is the probability that each face turns up exactly once? [4 MARKS] e) Suppose in a certain shipment of 250 Pentium processors there are 17 defective processors. A quality control consultant randomly collects 5 processors for inspection to determine whether or not they are defective. Let X denote the number of defectives in the sample. Find the probability of exactly 3 defectives in the sample, [2 MARKS] ii. Find the probability that there are at most 2 defectives in the sample [3 MARKS]