Suppose S={1,2,3,4, . . . ,2n}. Consider the following experiment in which we draw elements with replacement with P(S). We would like to draw elements in ascending cardinality and sets with the same amount of odd and even numbers. So we'll start by drawing at random until we get an empty set, then keep going until we get a set with one even and one odd number (after having gotten the empty set), then continue drawing until we have a set of two evens and two odds, and so on. We repeat this procedure until we get a set of n evens and n odds (after having gotten all the other even cardinalities). What is the expected total number of times we will draw a set during this whole process? Final answer is a sum of n and an index only, not a closed-form solution