Suppose that I have the set {01, b, c, d, e, f, g, h, 1'}. Without repeating digits, a) How many 6-Ietter \"words\" (i.e. unique rearrangements of letters) can I make from this set? b) Of those 6letter words, how many contain exactly one vowel? A class of 20 students wants to elect a committee consisting of a president, a vice president, a treasurer, and 4 secretaries. How many different committees can be formed? (Note: The secretary positions are all identical.) How many bit strings (i.e. sequences of Us and ls) of length 15 begin with 010 OR end with 101 (or both)? Suppose I am dealt a 5-card hand, from a regular deck of 52 cards. What is the probability that I am dealt: a) at least three cards with the same value e.g. (9,9,9,3,4), (4,4,4,4,5), etc. b) at least two cards with the same value e.g. (2,2,4,5,6), (Q,Q,Q,2,3), (2,2,4,4,5), etc. 5. Let A,B be events, where P(A n BC) = 0.2 and P(AC n B\") = 0.3. a) What is P(B)? (Note: There is not enough information here to draw a complete Venn diagram, but you have enough information to calculate P(B)) b) Suppose now that A and B are independent. Calculate P(A n B)