1. (4 pts) Consider all bit strings of length four. a) How many possible values are there without restriction? b) How many begin with 1? c) How many begin with 1 and end with 1? d) How many begin with 1 or end with 1? 2. (8 pts) Suppose that a "word" is any string of four letters. Repeated letters are allowed. For our purposes, vowels are the letters a, e, i, o, and u. a) How many words are there? Note - these don't have to be valid English words. b) How many words have no vowels? c) How many words have only vowels? d) How many words begin with a vowel? e) How many words have exactly one vowel? 4. (6 pts) Consider an ordinary deck of 52 playing cards with four suits (hearts, spades, diamonds, clubs) and 13 ranks in each suit (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K). You pick cards from the deck one at a time without replacement. What is the minimum number of cards you must pick in order to guarantee that you get: a) a pair of any rank, b) a pair of aces, and c) all four aces. 5. (2 pts) Consider the binomial theorem to expand (2x + 4y)*. What is the coefficient of the xy term? You must illustrate use of the binomial theorem for full credit