Water Pollution An environmental agency is analyzing water samples from 80 lakes for

Problem 2E When you calculate the number of combinations of r objects taken from a group of n objects, what are you counting? Give an example.

Problem 1E When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? Give an example.

Problem 62EC Cards In Exercise, you are dealt a hand of five cards from a standard deck of 52 playing cards. Find the probability of being dealt three of a kind (the other two cards are different from each other)

Problem 1UAE Assuming That Probability Has a “Memory” A “Daily Number” lottery has a three-digit number from 000 to 999. You buy one ticket each day. Your number is 389. (a) What is the probability of winning next Tuesday and Wednesday? ________________ (b) You won on Tuesday. What is the probability of winning on Wednesday? ________________ (c) You did not win on Tuesday. What is the probability of winning on Wednesday?

Problem 3E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. A combination is an ordered arrangement of objects.

Problem 2UAE Adding Probabilities Incorrectly A town has a population of 500 people. The probability that a randomly chosen person owns a pickup truck is 0.25 and the probability that a randomly chosen person owns an SUV is 0.30. What can you say about the probability that a randomly chosen person owns a pickup truck or an SUV? Could this probability be 0.55? Could it be 0.60? Explain your reasoning.

Problem 4E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. The number of different ordered arrangements of n distinct objects is n!.

Problem 6E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 7C5 = 7C2

Problem 5E True or False? In Exercise, determine whether the statement is true or false. If it is false, rewrite it as a true statement. When you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.

Problem 8E In Exercise, perform the indicated calculation. 16P2

Problem 7E In Exercise, perform the indicated calculation. 9P5

In Exercises 7–14, perform the indicated calculation. \(\frac{ _{8}C_{4}}{_{12}C_{6}}\) Equation Transcription: Text Transcription: frac{ _{8}C_{4}}{_{12}C_{6}}

Problem 9E In Exercise, perform the indicated calculation. 8C3

In Exercises 7–14, perform the indicated calculation. \(\frac{_{10}C_{7}}{_{14}C_{7}}\) Equation Transcription: Text Transcription: frac{_{10}C_{7}}{_{14}C_{7}}

Problem 10E In Exercise, perform the indicated calculation. 21C8

In Exercises 7–14, perform the indicated calculation. \(\frac{_{7}P_3} {_{12}P_4}\) ________________ Equation Transcription: Text Transcription: frac{_{7}P_3} {_{12}P_4}

In Exercises 7–14, perform the indicated calculation. \(\frac{{ }_{6} P_{2}}{{ }_{11} P_{3}}\) ________________ Equation Transcription: Text Transcription: frac{_{6}P_2}{_{11}P_{3}}

Problem 15E In Exercise, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways eight cars can line up in a row for a car wash

Problem 16E In Exercise, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways a four-member committee can be chosen from 10 people

Problem 19E Video Games You have seven different video games. How many different ways can you arrange the games side by side on a shelf?

Problem 17E In Exercise, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning. The number of ways 2 captains can be chosen from 28 players on a lacrosse team

Problem 18E In Exercise, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning. The number of four-letter passwords that can be created when no letter can be repeated

Problem 20E Skiing Eight people compete in a downhill ski race. Assuming that there are no ties, in how many different orders can the skiers finish?

Problem 21E Security Code In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security code?

Problem 23E Footrace There are 50 runners in a race. How many ways can the runners finish first, second, and third?

Problem 22E Starting Lineup The starting lineup for a softball team consists of 10 players. How many different batting orders are possible using the starting lineup?

Problem 24E Singing Competition There are 16 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth?

Problem 26E Archaeology Club An archaeology club has 38 members. How many different ways can the club select a president, vice-president, treasurer, and secretary?

Problem 27E Bracelets You are putting 4 spacers, 10 gold charms, and 8 silver charms on a bracelet. In how many distinguishable ways can the spacers and charms be put on the bracelet?

Problem 25E Playlist A DJ is preparing a playlist of 24 songs. How many different ways can the DJ choose the first six songs?

Problem 28E Necklaces You are putting 9 pieces of blue beach glass, 3 pieces of red beach glass, and 7 pieces of green beach glass on a necklace. In how many distinguishable ways can the beach glass be put on the necklace?

Problem 29E Letters In how many distinguishable ways can the letters in the word statistics be written?

Problem 30E Computer Science A byte is a sequence of eight bits. A bit can be a 0 or a 1. In how many distinguishable ways can you have a byte with five 0’s and three 1’s?

Problem 31E Experimental Group In order to conduct an experiment, 4 subjects are randomly selected from a group of 20 subjects. How many different groups of four subjects are possible?

Problem 32E Jury Selection From a group of 40 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected?

Problem 33E Students A class has 30 students. In how many different ways can five students form a group for an activity? (Assume the order of the students is not important.)

Problem 36E Menu A restaurant offers a dinner special that lets you choose from 12 entrees, 10 side dishes, and 6 desserts. You can choose one entree, two side dishes, and one dessert. How many different meals are possible?

Problem 35E Menu A restaurant offers a dinner special that lets you choose from 10 entrees, 8 side dishes, and 13 desserts. You can choose one entree, one side dish, and two desserts. How many different meals are possible?

Problem 37E Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Using technology, how many ways could one polluted lake and five non-polluted lakes be chosen?

Problem 34E Lottery Number Selection A lottery has 52 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)

Problem 38E Soil Contamination An environmental agency is analyzing soil samples from 50 farms for lead contamination. Eight of the farms have dangerously high levels of lead. Ten farms are randomly selected from the sample. Using technology, how many ways could two contaminated farms and eight noncontaminated farms be chosen?

Problem 42E Pizza Toppings A pizza shop offers nine toppings. No topping is used more than once. What is the probability that the toppings on a three-topping pizza are pepperoni, onions, and mushrooms?

Problem 40E Senate Subcommittee The U.S. Senate Subcommittee on Fiscal Responsibility and Economic Growth has five members. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the chairman and the ranking member? (Source: United States Senate)

Problem 39E Senate Committee The U.S. Senate Select Committee on Ethics has six members. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the chairman and vice chairman? (Source: United States Senate)

Problem 41E Horse Race A horse race has 12 entries. Assuming that there are no ties, what is the probability that the three horses owned by one person finish first, second, and third?

Problem 43E Jukebox You look over the songs on a jukebox and determine that you like 15 of the 56 songs. (a) What is the probability that you like the next three songs that are played? (Assume a song cannot be repeated.) ________________ (b) What is the probability that you do not like the next three songs that are played? (Assume a song cannot be repeated.)

Problem 44E Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team. (a) What is the probability that all of the offices are filled by members of the debate team? ________________ (b) What is the probability that none of the offices are filled by members of the debate team?

In Exercises 45–48, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 4 people at random from a group of 1200. What is the probability that all four would rate their financial shape as excellent? (Make the assumption that the 1200 people are represented by the pie chart.)

In Exercises 45–48, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 10 people at random from a group of 1200. What is the probability that all 10 would rate their financial shape as poor? (Make the assumption that the 1200 people are represented by the pie chart.)

Problem 49E Lottery In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. (a) How many ways can 5 numbers be chosen from 40 numbers? ________________ (b) You purchase one lottery ticket. What is the probability that you will win the top prize?

In Exercises 45–48, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 55 people at random from a group of 500. What is the probability that none of the 55 people would rate their financial shape as good? (Make the assumption that the 500 people are represented by the pie chart.)

In Exercises 45–48, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 80 people at random from a group of 500. What is the probability that none of the 80 people would rate their financial shape as fair? (Make the assumption that the 500 people are represented by the pie chart.)

Problem 50E Committee A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. (a) Use technology to find the number of ways 15 employees can be chosen from 200. ________________ (b) Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities. ________________ (c) What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)? ________________ (d) Does your answer to part (c) indicate that the committee selection is biased? Explain your reasoning.

Problem 51E Warehouse In Exercise, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing six first-shift workers.

Problem 53E Warehouse In Exercise, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing four second-shift workers.

Problem 56EC Defective Units A shipment of 20 keyboards contains 3 defective units. A company buys four of these units. What is the probability of the company buying at least three nondefective units?

Problem 52E Warehouse In Exercise, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing three first-shift workers.

Problem 54E Warehouse In Exercise, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing seven second-shift workers.

Problem 55EC Defective Units A shipment of 10 microwave ovens contains 2 defective units. A restaurant buys three of these units. What is the probability of the restaurant buying at least two nondefective units?

Problem 57EC Employee Selection Four sales representatives for a company are to be chosen at random to participate in a training program. The company has eight sales representatives, two in each of four regions. What is the probability that the four sales representatives chosen to participate in the training program will be from only two of the four regions?

Problem 58EC Employee Selection In Exercise, what is the probability that the four sales representatives chosen to participate in the training program will be from only three of the four regions? Exercise Employee Selection Four sales representatives for a company are to be chosen at random to participate in a training program. The company has eight sales representatives, two in each of four regions. What is the probability that the four sales representatives chosen to participate in the training program will be from only two of the four regions?

Problem 59EC Cards In Exercise, you are dealt a hand of five cards from a standard deck of 52 playing cards. Find the probability of being dealt two clubs and one of each of the other three suits.

Problem 60EC Cards In Exercise, you are dealt a hand of five cards from a standard deck of 52 playing cards. Find the probability of being dealt four of a kind.

Problem 61EC Cards In Exercise, you are dealt a hand of five cards from a standard deck of 52 playing cards.Find the probability of being dealt a full house (three of one kind and two of another kind).

When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? Give an example.

When you calculate the number of combinations of r objects taken from a group of n objects, what are you counting? Give an example.

True or False? In Exercises 3 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.A combination is an ordered arrangement of objects.

True or False? In Exercises 3 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.. The number of different ordered arrangements of n distinct objects is n!.

True or False? In Exercises 3 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.When you divide the number of permutations of 11 objects taken 3 at a time by 3!, you will get the number of combinations of 11 objects taken 3 at a time.

True or False? In Exercises 3 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 7C5 = 7C2

In Exercises 714, perform the indicated calculation. . 9P5

In Exercises 714, perform the indicated calculation. 16P2

In Exercises 714, perform the indicated calculation. 8C3

In Exercises 714, perform the indicated calculation.21C8

In Exercises 714, perform the indicated calculation. 8C4 12C6

In Exercises 714, perform the indicated calculation. . 10C7 14C7

In Exercises 714, perform the indicated calculation. 6P2 11P3

In Exercises 714, perform the indicated calculation.7P3 12P4

In Exercises 1518, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.The number of ways eight cars can line up in a row for a car wash

In Exercises 1518, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.The number of ways a four-member committee can be chosen from 10 people

In Exercises 1518, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.The number of ways 2 captains can be chosen from 28 players on a lacrosse team

In Exercises 1518, determine whether the situation involves permutations, combinations, or neither. Explain your reasoning.The number of four-letter passwords that can be created when no letter can be repeated

Video Games You have seven different video games. How many different ways can you arrange the games side by side on a shelf?

Skiing Eight people compete in a downhill ski race. Assuming that there are no ties, in how many different orders can the skiers finish?

Security Code In how many ways can the letters A, B, C, D, E, and F be arranged for a six-letter security code?

. Starting Lineup The starting lineup for a softball team consists of 10 players. How many different batting orders are possible using the starting lineup?

Footrace There are 50 runners in a race. How many ways can the runners finish first, second, and third?

Singing Competition There are 16 finalists in a singing competition. The top five singers receive prizes. How many ways can the singers finish first through fifth?

Playlist A DJ is preparing a playlist of 24 songs. How many different ways can the DJ choose the first six songs?

Archaeology Club An archaeology club has 38 members. How many different ways can the club select a president, vice-president, treasurer, and secretary?

Bracelets You are putting 4 spacers, 10 gold charms, and 8 silver charms on a bracelet. In how many distinguishable ways can the spacers and charms be put on the bracelet?

Necklaces You are putting 9 pieces of blue beach glass, 3 pieces of red beach glass, and 7 pieces of green beach glass on a necklace. In how many distinguishable ways can the beach glass be put on the necklace?

Letters In how many distinguishable ways can the letters in the word statistics be written?

. Computer Science A byte is a sequence of eight bits. A bit can be a 0 or a 1. In how many distinguishable ways can you have a byte with five 0s and three 1s?

Experimental Group In order to conduct an experiment, 4 subjects are randomly selected from a group of 20 subjects. How many different groups of four subjects are possible?

Jury Selection From a group of 40 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected?

Students A class has 30 students. In how many different ways can five students form a group for an activity? (Assume the order of the students is not important.)

Lottery Number Selection A lottery has 52 numbers. In how many different ways can 6 of the numbers be selected? (Assume that order of selection is not important.)

Menu A restaurant offers a dinner special that lets you choose from 10 entres, 8 side dishes, and 13 desserts. You can choose one entre, one side dish, and two desserts. How many different meals are possible?

Menu A restaurant offers a dinner special that lets you choose from 12 entres, 10 side dishes, and 6 desserts. You can choose one entre, two side dishes, and one dessert. How many different meals are possible?

Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Using technology, how many ways could one polluted lake and five non-polluted lakes be chosen?

Soil Contamination An environmental agency is analyzing soil samples from 50 farms for lead contamination. Eight of the farms have dangerously high levels of lead. Ten farms are randomly selected from the sample. Using technology, how many ways could two contaminated farms and eight noncontaminated farms be chosen?

. Senate Committee The U.S. Senate Select Committee on Ethics has six members. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the chairman and vice chairman? (Source: United States Senate)

Senate Subcommittee The U.S. Senate Subcommittee on Fiscal Responsibility and Economic Growth has five members. Each member is equally likely to serve in any of the positions. What is the probability of randomly selecting the chairman and the ranking member? (Source: United States Senate)

Horse Race A horse race has 12 entries. Assuming that there are no ties, what is the probability that the three horses owned by one person finish first, second, and third?

Pizza Toppings A pizza shop offers nine toppings. No topping is used more than once. What is the probability that the toppings on a three-topping pizza are pepperoni, onions, and mushrooms?

Jukebox You look over the songs on a jukebox and determine that you like 15 of the 56 songs. (a) What is the probability that you like the next three songs that are played? (Assume a song cannot be repeated.) (b) What is the probability that you do not like the next three songs that are played? (Assume a song cannot be repeated.)

Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team. (a) What is the probability that all of the offices are filled by members of the debate team? (b) What is the probability that none of the offices are filled by members of the debate team?

Financial Shape In Exercises 4548, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center)You choose 4 people at random from a group of 1200. What is the probability that all four would rate their financial shape as excellent? (Make the assumption that the 1200 people are represented by the pie chart.)

Financial Shape In Exercises 4548, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 10 people at random from a group of 1200. What is the probability that all 10 would rate their financial shape as poor? (Make the assumption that the 1200 people are represented by the pie chart.)

Financial Shape In Exercises 4548, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 80 people at random from a group of 500. What is the probability that none of the 80 people would rate their financial shape as fair? (Make the assumption that the 500 people are represented by the pie chart.)

Financial Shape In Exercises 4548, use the pie chart, which shows how U.S. adults rate their financial shape. (Source: Pew Research Center) You choose 55 people at random from a group of 500. What is the probability that none of the 55 people would rate their financial shape as good? (Make the assumption that the 500 people are represented by the pie chart.)

Lottery In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. (a) How many ways can 5 numbers be chosen from 40 numbers? (b) You purchase one lottery ticket. What is the probability that you will win the top prize?

Committee A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. (a) Use technology to find the number of ways 15 employees can be chosen from 200. (b) Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities. (c) What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)? (d) Does your answer to part (c) indicate that the committee selection is biased? Explain your reasoning

Warehouse In Exercises 5154, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment.Find the probability of choosing six first-shift workers.

Warehouse In Exercises 5154, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment.Find the probability of choosing three first-shift workers.

Warehouse In Exercises 5154, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment.Find the probability of choosing four second-shift workers.

Warehouse In Exercises 5154, a warehouse employs 24 workers on first shift and 17 workers on second shift. Eight workers are chosen at random to be interviewed about the work environment.Find the probability of choosing seven second-shift workers.

Defective Units A shipment of 10 microwave ovens contains 2 defective units. A restaurant buys three of these units. What is the probability of the restaurant buying at least two nondefective units?

Defective Units A shipment of 20 keyboards contains 3 defective units. A company buys four of these units. What is the probability of the company buying at least three nondefective units?

Employee Selection Four sales representatives for a company are to be chosen at random to participate in a training program. The company has eight sales representatives, two in each of four regions. What is the probability that the four sales representatives chosen to participate in the training program will be from only two of the four regions?

Employee Selection In Exercise 57, what is the probability that the four sales representatives chosen to participate in the training program will be from only three of the four regions?

Cards In Exercises 5962, you are dealt a hand of five cards from a standard deck of 52 playing cards.Find the probability of being dealt two clubs and one of each of the other three suits.

Cards In Exercises 5962, you are dealt a hand of five cards from a standard deck of 52 playing cards.Find the probability of being dealt four of a kind.

Cards In Exercises 5962, you are dealt a hand of five cards from a standard deck of 52 playing cards.Find the probability of being dealt a full house (three of one kind and two of another kind).

Cards In Exercises 5962, you are dealt a hand of five cards from a standard deck of 52 playing cards. Find the probability of being dealt three of a kind (the other two cards are different from each other).