You have 10 pairs of socks. 3 pairs are bright stripes, 5 pairs are checkered designs, and 2 pairs are solid colors. Both socks in a pair are identical, but each of the pairs are distinct from each other. A pair of socks is "properly matched" if they are from the same pair. A pair of socks is "fashionably mismatched" if they are from different pairs, but from the same group (for example, two bright stripe socks that aren't from the same pair are fashionably mismatched; but a solid color sock and a checkered sock isn't). You (uniformly) randomly pair the socks with each other. In each of these problems clearly define any random variables you need. (a) What is the expected number of pairs of properly matched socks? [7 points] (b) What is the expected number of pairs of fashionably mismatched socks? [7 points]