1. (10 pts) Consider the set of words (character strings) consisting "a" and "b", e.g. "aaba", "bbaba". (a) How many words have length 10 in this set? (b) A word is called special if it is lexicographically strictly smaller than any of its proper suffixes. For example, "ababb" is special. How many words of length 10 are special? 2. (10 pts) Suppose that two identical decks of 52 distinct cards (total 104 cards) are mixed together and are randomly divided into 13 hands of 8 cards each. What is the probability that no hand has more than one ace