Math 140: Quiz 12,13,14 1 Quiz 12 Problem 1: The characters in a license plate in a certain state consists of 7 characters. The first two characters must be numbers from 0 through 9, and the last 5 characters are capital letters. A license plate is generated at random with all possible characters equally likely to appear. a. What is the probability that the first two characters of the license plate are 92? b. What is the probability that the last four letters in the license plate are \"MATH\"? Problem 2: Suppose any 7 digits can be used to form a telephone number. a. How many telephone numbers don't have any repeated digits (adjacent or otherwise)? b. What is the probability that a randomly chosen telephone number has at least one repeated digit? Math 140: Quiz 12,13,14 2 Quiz 13 Problem 1: How many cards must you pick from a standard deck of 52 cards to be certain to have a pair of cards of the same suit? Problem 2: A certain college class has 40 students whose ages are in the range of 17 34. You want to make a bet that at least x of the students are the same age. What is the largest value for x that you can choose to be certain. Problem 3: How many integers from 100 through 999 must you pick randomly to be certain that at least two of them have a common digit? (For example, 256 and 513 have the common digit 5.) Math 140: Quiz 12,13,14 3 Quiz 14 Problem 1: From a group of 12 people, how many ways are there of forming a committee of 5 people? (order of selection doesn't matter; i.e. the committee consisting of persons A, B, C, D, and E is the same as the committee consisting of persons E,A,D,C,B) Problem 2: How many different 5 card hands from a standard 52 card deck consist of a threeof-a-kind (but not a full house)? (Recall a three-of-a-kind consists of three cards with the same face value; for example 5755K is a three-of-a-kind with three 50 s. A full house is of the form AAABB.) Problem 3: What is the probability that a randomly chosen set of 5 cards from a standard 52 card deck is a straight or a straight flush? (A straight consists of 5 face values in sequential order. The order of face cards are 2,3,4,5,6,7,8,9, (J)ack, (Q)ueen, (K)ing, (A)ce. Don't count those straights that \"wrap around the corner\"; i.e. 89JQK is a straight, but KA234 is not. As a special rule, the Ace can be counted as 1 when creating a straight; i.e. A2345 is a straight. A straight flush is a straight that consists of cards from the same suit: clubs, spades, diamonds or hearts)