Problem 1SP: A pizza can be made from either thick or thin crust, and a choice of 6 toppings. How many different... Problem 2SP: A code for an alarm system is made up of two letters, followed by four digits. How many codes can be... Problem 3SP: A quiz has four true/false questions and six multiple-choice questions. The multiple-choice... Problem 4SP: a. In how many ways can 7 different books be arranged on a bookshelf? b. Determine the number of... Problem 5SP: Determine the number of ways that 2 students from a group of 4 students can be selected to hold the... Problem 6SP: A judge at the County Fair must give blue, red, and white ribbons for first-, second-, and... Problem 7SP: Suppose that 20 people enter a raffle. a. In how many ways can four different people among the 20 be... Problem 8SP: The California lottery game “Fantasy 5 � offers a grand prize to a player who selects the... Problem 9SP: The coach of a co-ed softball team must select 4 women and 5 men from a group of 7 women and 10 men... Problem 1PE: The fundamental of indicates that if one event can occur in m different ways, and a second event... Problem 2PE: If n items are arranged in order, then each arrangement is called a of n items. Problem 3PE: The number of ways that n distinguishable items can be arranged in various orders is . Problem 4PE: Consider a set of n elements of which one element is repeated r times. Then the number of... Problem 5PE: Suppose that n represents the number of distinct elements in a group from which r elements will be... Problem 6PE: Suppose that n represents the number of elements in a group from which r elements will be selected... Problem 7PE: The number of permutations of n elements taken r at a time is denoted by nPr and is computed by nPr=... Problem 8PE: The number of combinations of n elements taken r at a time is denoted by nCr and is computed by . Problem 9PE: For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is... Problem 10PE: For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is... Problem 11PE: For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is... Problem 12PE: For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is... Problem 13PE: For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is... Problem 14PE: For Exercises 9-14, consider the set of integers from 1 to 20 , inclusive. If one number is... Problem 15PE Problem 16PE: Debbie travels several times a year for her job. She takes 4 pairs of slacks, 6 blouses, and 4... Problem 17PE: A license plate has 3 letters followed by 3 digits. a. How many license plates can be made if there... Problem 18PE: A security company requires its employees to have a 7 -character computer password that must consist... Problem 19PE: The call letters for a radio station must begin with either K or W . a. How many 4 -letter... Problem 20PE: An employee identification code for a hospital consists of 2 letters from the set A,B,C,D followed... Problem 21PE: An online survey is used to monitor customer service. The survey consists of 14 questions. Ten... Problem 22PE: A test consists of 3 multiple-choice questions, each with four possible responses, and 7 true/false... Problem 23PE: On a computer, 1 bit is a single binary digit and has two possible outcomes: either 1 or 0 . One... Problem 24PE: Older models of garage door remote controls have a sequence of 10 switches that are individually... Problem 25PE: a. In how many ways can the letters in the word FLORIDA be arranged? (See Example 4) b. In how many... Problem 26PE: a. In how many ways can the letters in the word XRAY be arranged? b. In how many ways can the... Problem 27PE: In how many ways can the word WRONG be misspelled? Problem 28PE: In how many ways can the word EXACTLY be misspelled? Problem 29PE: A delivery truck must make 4 stops at locations A,B,C , and D . Over several weeks, management asks... Problem 30PE: In how many ways can 6 people in a family be lined up for a photograph? Problem 31PE: For Exercises 31-36, evaluate nPr . 6P4 Problem 32PE: For Exercises 31-36, evaluate nPr . 8P5 Problem 33PE: For Exercises 31-36, evaluate nPr . 12P2 Problem 34PE: For Exercises 31-36, evaluate nPr . 11P3 Problem 35PE: For Exercises 31-36, evaluate nPr . 9P9 Problem 36PE: For Exercises 31-36, evaluate nPr . 5P5 Problem 37PE: Evaluate 20P3 and interpret its meaning. Problem 38PE: Evaluate 15P6 and interpret its meaning. Problem 39PE Problem 40PE: For Exercises 39-44, evaluate nCr . 8C5 Problem 41PE: For Exercises 39-44, evaluate nCr . 12C2 Problem 42PE Problem 43PE Problem 44PE: For Exercises 39-44, evaluate nCr . 5C5 Problem 45PE: Evaluate 20C3 and interpret its meaning. Problem 46PE: Evaluate 15C6 and interpret its meaning. Problem 47PE: Given A,B,C , a. List all the permutations of two elements from the set. (See Example 5) b. List all... Problem 48PE: Given W,X,Y,Z , a. List all the permutations of three elements from the set. b. List all the... Problem 49PE: Suppose that 9 horses run a race. How many first-, second-, and third-place finishes are possible?... Problem 50PE: In how many ways can a judge award blue, red, and yellow ribbons to 3 films at a film festival if... Problem 51PE: a. In a drama class, 5 students are to be selected from 24 students to perform a synchronized dance,... Problem 52PE: a. There are 100 members of the U.S. Senate. Suppose that 4 senators currently serve on a committee,... Problem 53PE: A chess tournament has 16 players. Every player plays every other player exactly once. How many... Problem 54PE: Suppose that a tennis tournament has 64 players. In how many ways can a pairing for a first-round... Problem 55PE: In the Minnesota Lotto game “Gopher 5 � a player wins the grand prize by choosing the same group... Problem 56PE: In the New York state lottery game “Lotto� a player wins the grand prize by choosing the same... Problem 57PE: At a ballroom dance lesson, the instructor chooses 3 men and 3 women to demonstrate a new pattern.... Problem 58PE: A committee of 4 men and 4 women is to be made from a group of 12 men and 9 women. In how many ways... Problem 59PE: In a “Pick-4 � game, a player wins a prize for matching a 4-digit number from 0000 to 9999 with... Problem 60PE: In a “Numbers� game, a player wins a prize for matching a 3-digit number from 000 to 999 with... Problem 61PE: Liza is a basketball coach and must select 5 players out of 12 players to start a game. In how many... Problem 62PE: Jean has a list of 8 books that she knows she must read for a class in the upcoming fall semester of... Problem 63PE: In how many ways can a manager assign 5 employees at a coffee shop to 5 different tasks? Assume that... Problem 64PE: In how many ways can a class of 12 kindergarten children line up at the cafeteria? Problem 65PE: Twenty batteries have been sitting in a drawer for 2yr . There are 4 dead batteries among the 20 .... Problem 66PE: There are 30 seeds in a package. Five seeds are defective (will not germinate). If four seeds are... Problem 67PE: A “combination� lock is opened by correctly “dialing� 3 numbers from 0 to 39 , inclusive.... Problem 68PE: A palindrome is an arrangement of letters that reads the same way forward and backward. For example,... Problem 69PE: A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the... Problem 70PE: A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the... Problem 71PE: A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the... Problem 72PE: A line segment connecting any two nonadjacent vertices of a polygon is called a diagonal of the... Problem 73PE: For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed... Problem 74PE: For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed... Problem 75PE: For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed... Problem 76PE: For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed... Problem 77PE: For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed... Problem 78PE: For Exercises 73-78, consider the set of numbers 0,1,2,3,4,5 . How many 3-digit codes can be formed... Problem 79PE: In Exercise 103 from Section 11.3 , we learned that if a fair coin is flipped n times, the number of... Problem 80PE: Social Security numbers assigned in the United States are comprised of 9 digits of the form -- .... Problem 81PE: Airlines often oversell seats on an airplane. This is done so that the seats for the few passengers... Problem 82PE: In how many ways can a platoon leader select 4 soldiers among 15 soldiers to secure a building? Problem 83PE: A car can comfortably hold a family of five. If two people among the five can drive, how many... Problem 84PE: A television station must play twelve 30-sec commercials during a half-hour show. In how many ways... Problem 85PE: Consider a horse race with 8 horses. Explain how the fundamental principle of counting or the... Problem 86PE: Explain why the number of combinations of n items taken r at a time can be computed by nPrr! . Problem 87PE: Three biology books, 4 math books, and 2 physics books are to be placed on a bookshelf where the... Problem 88PE: A softball team has 9 players consisting of 3 women and 6 men. In how many ways can the coach... format_list_bulleted