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Let n > 1 be an integer and let S = {1,...,n}. Use the Product Rule (Lecture 2) to answer these questions. 1. How many ways are there to partition S into four sets X, Y, Z, and W? (Partition means that each element of S is contained in exactly one of X, Y, Z, or W (and we allow any of these four sets to be empty)] 2. Hw many ways are there to pick three pairwise disjoint sets X, Y, Z CS? [Pairwise disjoini means that each element of S appears in at most one of X, Y, or 2.] 3. How many ways are there to make three subsets X, Y, Z CS so that any element of S appears in at most 2 of the three sets