Ca) How many ways are there to partition the set {2, 4, 6, ...,20} into three unordered subsets of sizes 3,3, and 4, respectively. b) Let (21, 22, ..., 135) be a sequence consisting of the integers 1 to 35, in some random order. Show that there must be five consecutive Ti that are all less than 30. (c) What is the probability that an integer chosen randomly from {1,2,..., 2020} is divis- ible by one or both of 2 and 3. d) Let X be an object that has exactly three symmetries, so its symmetry group Sym(X) has exactly three elements. Show that X is chiral