03 (17 points) The number 6, 469, 693, 230 has 10 prime factors. Suppose we select a random subset of 6 of these prime factors (without replacement) and multiply them together. (a) [3 points] Describe the sample space and how many elements are in it? (b) [3 points] What is the probability that the product is even? (c) [3 points] What is the probability that the product is divisible by 10? (d) [3 points] What is the probability that the primes are drawn in (strictly) increasing order (for example 3 before 7, 7 before 23 etc.) (e) [5 points] Use R to determine the approximate probability that the product is less than 100000. Q4 (15 points) Repeat Question 3 where the primes are selected with replacement