Permutations and Combinations Questions and Answers

A person can order a new car with a choice of 12 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?

A restaurant offers the following limited lunch menu. Main Courses Vegetables Beverages Desserts Turkey, Spaghetti, Meatloaf, Shrimp, Hamburger Corn, Green Beans Coffee, Tea, Milk, Soda Ice Cream, Brownies If one item is selected from each of the four groups, in how many ways can a meal be ordere There are ways a meal can be ordered. .....

11 A certain lottery has 30 numbers. In how many different ways can 4 of the numbers be selected? (Assume that order of selection is not important.) There are different ways the numbers can be selected. *****

Leanne is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, 5 appetizers, and 3 desserts, but she does not have time to cook. She can choose from 9 bottled drinks, 9 frozen appetizers, and 12 prepared desserts at the supermarket. How many different ways can Leanne pick the food and drinks to serve at the bridal shower?

You are using a local home remodeling company to remodel your kitchen. They have 13 different cabinet door styles, 10 countertop choices, and 19 different types of flooring. How many different kitchen remodels could be done using these material choices?

Car Rental In Exercises 27-30, a car rental agency has 10 midsized and 15 compact cars on its lot, from which 6 will be selected. Assuming that each car is equally likely to be selected and the cars are selected at random, deter- mine the probability (as a decimal number rounded to four decimal places) that the cars selected consist of 27. all midsized cars. 28. 2 midsized cars and 4 compact cars. 29. 3 midsized cars and 3 compact cars. 30. at least 1 compact car.

An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 3 novels, 5 plays, 8 poetry books, and 7 nonfiction books. Step 1 of 2: If she wants to include no more than 3 plays, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place.

A cube made of an unknown material has a height of 8 cm. The mass of the cube is 4255 g. Calculate the density of this cube. 6.648 g/cubic meter 53.188 g/cubic cm 21.3 g/cubic cm 8.311 g/cubic cm

Assuming that no questions are left unanswered, in how many ways can a five-question quiz with 4-choice multiple choice questions be answered?

According to The World Bank, only 9% of the population of Uganda had access to electricity as of 2009. Suppose we randomly sample 150 people in Uganda. Let X = the number of people in the sample who have access to electricity.

How can $40,000 be invested, part at 9% annual simple interest and the remainder at 11% annual simple interest, so that the interest earned by the two accounts will be equal? The amount to invest at 9% is $ .....

7 junior high classes will be chosen to participate in a school activities survey. There are 22 junior high classes in the school. In how many ways can the classes be chosen?

A computer password is 6 entries long. If the password must have 3 letters followed by 3 numbers with repetition of numbers and/or letters permitted, how many different passwords are possible?

You volunteer at the animal shelter. They are putting together a calendar with pictures of the animals to raise money and get more adoptions. They put you in charge of taking the pictures for April and May. For April, you need to take a picture with eight adult dogs. There are fifteen adult dogs at the shelter. In how many ways could you choose eight dogs? 15 8 6,435 259,459,200

Compute the permutations and combinations. From a committee consisting of 5 men and 6 women, a sub-committee is formed consisting of 4 men and 3 women. How many different subcommittees are possible? 100 360 600

Find the number of positive integers less than 100,000 whose digits are among 1, 2, 3, and 4. Hint: consider the possibilities for 5-digit, 4-digit, 3-digit, 2-digit, and 1-digit numbers and repetition of digits. 1,364 1,024 256

In a certain manufacturing plant, the first operation can be done on any one of five machines, the second operation on only one machine, the third operation on any one of six machines, and the fourth operation on either of two machines. Over how many routes can the raw material be processed? 14 56 60

The dial of a combination lock has all 26 letters of the alphabet on it. A combination is formed by dialing 3 different letters in a particular order. If the owner of the lock forgets the combination, how many trials may be needed to open the lock? 17,576 15,600 78

The ten students in a club are lined up in a row for a group photograph. How many different arrangements are possible if the club includes one set of identical triplets wearing matching clothes? 604,800 720 10,000,000

An electronic salesperson carries 6 identical amplifier tubes, 5 identical rectifiers, 2 identical condensers, and 4 identical relays. In how many different ways can these parts be arranged in a row? 6.5.2.4 17!/(6.5.2.4) 17!/(6!5!2!4!)

Find the value of the combination. A farmer buys three cows, two pigs, and ten sheep from a seller who has seven cows, four pigs, and ten sheep. Ho many choices of animals does he have? 54,264 210 42

Find the value of the combination. From a committee consisting of 8 men and 5 women, a subcommittee is formed consisting of 4 men and 3 women. How many different subcommittees are possible? 80 700 1,716

(c) Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? In a similar way as in Example 9.5.6, let A and B be the two team members who refuse to work together in a group. Thinking about the number of groups that contain A and not B, B and not A, and neither A nor B leads to the conclusion that the total number of groups of that can be chosen to work on the project is (d) Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project? As in Example 9.5.5, let A and B be the two team members who insist on working in a group together or not at all. How many groups contain both A and B? How many groups contain neither A nor B?

Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes. Drug A is to be given to 21 mice, drug B is to be given to another 21 mice, and the remaining 18 mice are to be used as controls. How many ways can the assignment of treatments to mice be made? (A single assignment involves specifying the treatment for each mouse-whether drug A, drug B, or no drug.) (Enter the exact number or an equivalent algebraic expression.)

Consider reordering the letters in the word TENNESSEE. Use the technique shown in Example 9.5.11 to answer the following questions. If the N's are placed first, how many ways are there to choose positions for them? If the E's are placed second, how many ways are there to choose positions for them? If the S's are placed third, how many ways are there to choose positions for them? If the T is placed fourth, how many ways are there to choose a position for it? So, the total number of ways to reorder the letters in the word TENNESSEE is

A nursing student can be assigned to one of five different floors each day depending on staffing needs. How many different ways can she be assigned during a 4-day work week? The nursing student can be assigned in ... different ways.

There are twenty students in a speech class and five speeches are given each day. What is the probability that Maria is randomly selected on the first day? 1,140/15,504 3,876/15,504 4,845/15,504 11,628/15,504

Use the multiplication principle to solve. A home improvement store website listed 246 different kinds of glass wall tile, 26 colors of acrylic grout, 12 kinds of mortar trowels, and 17 different kinds of mortar. How many ways are there to buy the products needed for a tile project?

A combination lock requires three selections of numbers, each from 1 through 33. Suppose the lock is constructed in such a way that no number may be used twice in a row, but the same number may occur both first and third. For example, 20 13 20 would be acceptable, but 20 20 13 would not. How many different combinations are possible? To answer this question, note that some combinations will consist of three different numbers, whereas in others the first and third numbers can be the same. The total number of combinations is

In a competition between players X and Y, the first player to win three games in a row or a total of four games wins. How many ways can the competition be played if X wins the first game and Y wins the second and third games? (Hint: Draw a tree.)

There are five lab rats (named A, B, C, D, E) that have been trained to play musical chairs, with five chairs in order one through five. How many possible orderings of the rats in the chairs are there? 120 720 60 20

Which scenario is a permutation? School spirit shirts can be ordered in sizes S, M, L, or XL They offer both short-sleeve shirts and long-sleeve shirts. How many different ways are there to order a school spirit shirt? At a car dealership, you can purchase a car, truck, or SUV. Each type of vehicle is offered in five colors. How many different ways are there to purchase a vehicle at the dealership? The ballot for student council is for president, vice president, secretary, and treasurer. There are a total of nine candidates for all the positions combined. The president will be the student with the most votes, vice president will be the one with the second highest number of votes, and so on. How many ways can the positions be filled? An ice cream parlor offers twenty-one varieties of ice cream. How many possible ways are there to choose three different scoops of ice cream for a banana split?

Which scenario uses the formula nPk =n!/(n-k)! to solve? There are eighteen players on a school soccer team. How many ways can two players be chosen as captain and co-captain? School spirit shirts can be ordered in sizes S, M, L, or XL. They offer both short-sleeve shirts and long-sleeve shirts. How many different ways are there to order a school spirit shirt? An ice cream parlor offers twenty-one varieties of ice cream. How many possible ways are there to choose three different scoops of ice cream for a banana split? At a car dealership, you can purchase a car, truck, or SUV. Each type of vehicle is offered in five colors. How many different ways are there to purchase a vehicle at the dealership?

Which scenarios are combinations? There are eighteen players on a school soccer team. How many ways can two players be chosen as captain and co-captain? School spirit shirts can be ordered in sizes S, M, L, or XL. They offer both short-sleeve shirts and long-sleeve shirts. How many different ways are there to order a school spirit shirt? Bingo games have seventy-five balls that are called out at random until a player calls bingo. Each ball is labeled 1 to 75. How many ways are there for picking five numbers? An ice cream parlor offers twenty-one varieties of ice cream. How many possible ways are there to choose three different scoops of Ice cream for a banana split? The ballot for student council is for president, vice president, secretary, and treasurer. There is a total of nine candidates for all the positions combined. The president will be the one with the most votes, vice president will be the one with the second highest number of votes, and so on. How many ways can the positions be filled?

The bacteria in a 8-liter container double every 4 minutes. After 53 minutes the container is full. How long did it take to fill a quarter of the container? Round the answer to the nearest tenth of a minute. A. 13.3 min B. 26.5 min C. 45.0 min D. 39.8 min

The numbers zero, one, two, three and four are used for racing numbers in a marathon. A racing number consists of five digits. What is the probability the first number is zero if repeats are allowed? Assume that each number is equally likely to be chosen. 1/3,125 1/5 4/3,125 4/5

You have tomato, cucumber, potato, corn, and squash seeds that you could plant in your garden. Youonly have room to plant 2 types of seeds. How many ways could you choose two types of seeds to plant? Do this by hand. 5 2 20 10

Fundamental Counting Principle conditions in the following problems. Hint: There are 10 choices for the digits and 26 choices for the letters

A bicycle lock has a four-digit code of which each digit is a number from 0 to 9. Which of the following expressions correctly represents the number of possible codes the lock can have? 9x8x7x6 10 x 9 x 8 x 7 9x9x9x9 10 x 10 x 10 x 10

Suzie is buying a new laptop for school and can select none, some, or all of the following choices of peripherals: a laser mouse, a DVD burner, a Web cam, or a jump drive. How many different selections of peripherals are possible for her laptop?

When testing for current in a cable with six color-coded wires, the author used a meter to test four wires at a time. How many different tests are required for every possible pairing of four wires? The number of tests required is DECIS

For a Halloween party, each guest can choose from the 15 different kinds of candy to have in a prize bag. If any number of candy types can be chosen, how many candy type combinations are possible?

A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For example, a phase I test of a specific drug involved only 7 subjects. Assume that we want to treat 7 healthy humans with this new drug and we have 11 suitable volunteers available. Complete parts (a) through (c) below. a. If the subjects are selected and treated in sequence, so that the trial is discontinued if anyone displays adverse effects, how many different sequential arrangements are possible if 7 people are selected from the 11 that are available? Choose the correct answer below. A. 1,663,200 B. 5,040 C. 39,916,800 D. 330 b. If 7 subjects are selected from the 11 that are available, and the 7 selected subjects are all treated at the same time, how many different treatment groups are possible?

A corporation must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO) It must also appoint a planning committee with three different members. There are 14 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below a. How many different ways can the officers be appointed? There are 24024 different ways to appoint the officers b. How many different ways can the committee be appointed? different ways to appoint the committee

For a Halloween party, each guest can choose from the 8 different kinds of candy to have in a prize bag. If any number of candy types can be chosen, how many candy type combinations are possible? Select the correct answer below: 64 128 256 40.320

A manager of a clothing store always orders 2 small T-shirts and 3 large T-shirts for every 4 medium T-shirts. The manager plans to order 24 medium T-shirts. How many small T-shirts and large T-shirts should the manager order? Show your work.

The number of hits to a website follows a Poisson process. Hits occur at the rate of 2.2 per minute between 7:00 P.M. and 9:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 8:34 P.M. and 8:41 PM. Interpret each result. (a) exactly seven (b) fewer than seven (c) at least seven

Douglas is going to visit 6 cities this summer. He will choose from 12 different cities and the order in which he visits the cities does not matter. How many different city combinations are possible for the summer travelling?

Josh is choosing between the 8 different types of chips in the vending machine. If any number of chips types can be chosen, how many chip type combinations are possible? Select the correct answer below: 64 128 256 40, 320

Raymond is working a word puzzle and is looking for four-letter "scrambles" from the clue word calculate. a) How many of the possible four letter scrambles contain four different letters? b) How many DIFFERENT 'words' contain two a's and one other pair of identical letters? c) What assumptions/conditions did you make for part b?