Permutations and Combinations Questions and Answers

Jason works as an administrative assistant for a local lawyer's office. The office is running low on pens and notepads, so he is asked to buy $150 worth of pens and notepads. Pens cost $1, and notepads cost $2. If the number of pens he buys is represented by x and the number of notepads he buys is represented by y, the situation can be given by x + 2y = 150, where 0 sxs 150, 0 sys 75 and x and y can take only integer values.

Suppose thirteen people qualify for a college cheerleading squad, eight are men and 5 are women. If a 6 member squad is selected, what is the probability that the squad will have exactly two male members. Select one: a. 8% b. 6.5% c. 25% d. 33%

Suppose we want to choose 2 colors, without replacement, from the 4 colors red, blue, green, and purple. (a)How many ways can this be done, if the order of the choices is taken into consideration? (b)How many ways can this be done, if the order of the choices is not taken into consideration?

A technology company is going to issue new ID codes to its employees. Each code will have two letters, followed by one digit, followed by one letter. The letters D, G, and Z and the digit 8 will not be used. So, there are 23 letters and 9 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?

A certain train has 11 cars that are being lined up on a track. One of the cars is the engine, and another is the caboose. The engine will be the first car in line. The caboose will be the last car in line. In how many ways can the cars be lined up?

Suppose we want to choose 5 letters, without replacement, from 9 distinct letters. (a) How many ways can this be done, if the order of the choices is not taken into consideration? (b) How many ways can this be done, if the order of the choices is taken into consideration?

Suppose we want to choose 5 colors, without replacement, from 14 distinct colors. (a) If the order of the choices is relevant, how many ways can this be done? (b) If the order of the choices is not relevant, how many ways can this be done?

Shen is putting 10 books in a row on his bookshelf. He will put one of the books, Gulliver's Travels, in the first spot. He will put another of the books, A Tale of Two Cities, in the last spot. In how many ways can he put the books on the shelf?

Bob is planning to pack 6 shirts and 3 pairs of pants for a trip. If he has 15 shirts and 8 pairs of pants to choose from, in how many ways can this be done? (Hint: Use the counting principle and order is not important!)

In an experiment, a fair coin is tossed 12 times and the face that appears (H for head or T for tail) for each toss is recorded. How many elements of the sample space will have no heads? How many elements of the sample space will have exactly one head? How many elements of the sample space will start and end with different faces and have a total of exactly two heads? How many elements of the sample space will start or end with a head and have an adjacent pair or triple of heads and include a total of exactly three heads?

The environment club is electing a president, vice president, and treasurer. How many different ways can the officers be chosen from the 6 members? A. 196 B. 180 C. 150 D. 120

A person can order a new car with a choice of 13 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?

An individual can be classified by gender as male, female, by hair color as black, blonde, brown, and by eye color as black, brown. a) How many different classifications are possible (for example, male, with black hair, and black eyes)?

In a given city, there are 5 body styles of cars. Any of the body styles can come in 1 of 4 colors. How many cars need to be on the city's streets to guarantee there are at least 2 cars with the same body style and color on the road? 20 626 1,025 21

While making up his schedule for spring semester, Tom complains that he doesn't have very many choices of schedule because of the general education requirements he has to meet. His advisor tells Tom that he has to take one course from each of English (4 choices), History (3 choices), Math/Stats (4 choices), Computer Science (4 choices), and general Science (4 choices). Does Tom have a legitimate gripe? (a) If every possible course is available at the time he's registering, how many possible schedules can he choose from (disregarding when the classes meet)? Tom can choose from possible schedules. (b) When trying to schedule, Tom finds that all but two of the English courses are closed, as are one History course and one general Science course. How many schedules does he have to choose from now? Tom now has different schedules to choose from.

Diana Baniak, searching for an Ecology class, knows that it must be in one of ten classrooms. Since the professor does not allow people to enter after the class has begun, and there is very little time left, she decides to try just five of the rooms at random. How many of the possible different selections of five rooms will succeed in locating the class? There are 120 successful selections.

ET A standard 52-card deck contains four aces, twelve face cards, thirteen hearts (all red), thirteen diamonds (all red), thirteen spades (all black), and thirteen clubs (all black). Of the 752,538,150 different eight-card hands possible, decide how many would consist of the following. (a) all clubs (b) all black cards (c) all aces (a) There are (Simplify your answer.) ways to have a hand with all clubs. .....

Yogi's picnic basket contains two types of lunch meat and four kinds of bread. Boo Boo's picnic basket contains five additional types of lunch meat and three additional kinds of bread. How many ways can Yogi and Boo Boo select one type of meat and one type of bread to make a sandwich?

DIRECTIONS: Read the facts carefully for each question. First answer, is it asking for a permutation, or a combination? Explain why. Then answer the question: 1/ Ben has 6 shirts, 4 ties, and 2 jackets. How many different outfits of a shirt, a tie, and a jacket can he choose?

How many ways can 2 men and 2 women be selected for a debate tournament if there are 10 male finalists and 11 female finalists?

A professor has five different tasks to assign, one to each of her five teaching assistants. In how many different ways could she make the assignments? There are ... different ways the professor could assign the tasks.

A Civil Air Patrol unit of fourteen members includes four officers. In how many ways can three members be selected for a search and rescue mission such that at least one officer is included? The number of ways is. (Simplify your answer.)

If license numbers consist of three letters followed by four digits, how many different licenses could be created having at least one letter or digit repeated? There are license plates that can be created.

Among the 2,598,960 possible 5-card poker hands from a standard 52-card deck, how many contain at least one king (complement of "no kings" )? Dealt from a standard deck, hands contain at least one king.

A doughnut shop has a special on its Mix-n-Match selection, which allows customers to select three doughnuts from the following varieties: frosted, apple cider, maple, Boston creme, plain, peanut butter, and chocolate. How many different Mix-n-Match selections are possible? [Hint: Consider when all three doughnuts are the same, two are the same, and none are the same.] There are possible selections. (Type a whole number.)

Katrina, Jim, Larry, Tyrone, Dawn, lan, and Maria have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. a. In how many ways can they arrive? b. In how many ways can Katrina arrive first and Maria last? c. Find the probability that Katrina will arrive first and Maria last. a. (Type an integer.) .....

In the exercise, use permutations, combinations, the fundamental counting principle, or other counting methods, as appropriate. How many different 5-card poker hands would only contain cards of a single suit?

In a group of 10 people, 4 of them will be selected to serve as members of a committee. How many ways can these 4 people be selected from the group of 10?

A committee of seven Congressmen will be selected from a group of eleven Democrats and four Republicans. Find the number of ways of obtaining a committee with exactly three Democrats. There are ... ways to have exactly three Democrats on the committee.

A contractor builds homes of 12 different models and presently has 3 lots to build on. In how many different ways can he arrange homes on these lots? Assume 3 different models will be built. The answer is arrangements. ▪▪▪▪▪

A baseball team has 3 pitchers, who only pitch, and 21 other players, all of whom can play any position other than pitcher. For Saturday's game, the coach has not yet determined which 9 players to use nor what the batting order will be, except that the pitcher will bat last. How many different batting orders may occur? There are ... different batting orders.

Television and radio stations use four call letters starting with W or K, such as WXYZ or KRLD. Assuming no repetitions in the second to fourth letters, how many four-letter sets are possible using either W or K and only the letters C to T? (Count all possibilities even though, practically, some may be inappropriate.) There are four-letter sets that can be formed.

The department of transportation is trying to figure out how many distinct license plates can be made with 8 characters, some letters and some digits. For example: XA12BN35. Should they calculate the permutations or combinations of the characters?

The lunch menu at Ma Kelly's Restaurant offers five entrees, four salads, and three desserts. If Rick always orders one of each, how many days can he eat lunch at the restaurant without repeating a meal? a. b. C. d. e. 30 15 20 60 12

Evaluate the expression. 13C5 13C5 =

Determine the number of combinations (subsets) of the following. 10 objects taken 6 at a time There are combinations of 10 objects taken 6 at a time.

In how many ways could nine people be divided into two groups of four people and one group of one person? Nine people could be divided into two groups of four people and one group of one person ... ways.

How many ways can a president, vice-president, secretary, and treasurer be chosen from a committee of 6 people? The number of ways to choose a president, vice-president, secretary, and treasurer is ....

A club is made up of the members listed below. Assuming that all members are eligible, but no one can hold more than one office, list and count the different ways the club could elect a president, a secretary, and a treasurer, if all three officers must be women. (Cathy, Dorothy, and Eileen are women, and the others are men.) N={Andrew, Ben, Cathy, Dorothy, Eileen) or, in abbreviated form N= {A, B, C, D, E). List the different ways the club could elect each group of officers. Choose the correct answer below. A. CDE, DCE, ECD B. CDA, CDB, CEA, CEB, DCA, DCB, DEA, DEB, ECA, ECB, EDA, EDB C. ACD, BCD, ACE, BCE, ADC, BDC, ADE, BDE, AEC, BEC, AED, BED, CAD, CBD, CAE, CBE, DAC, DBC, DAE, DBE, EAC, EBC, EAD, EBD, CDA, CDB, CEA, CEB, DCA, DCB, DEA, DEB, ECA, ECB, EDA, EDB D. ADE, AED, DAE, DEA, EAD, EDA E. CDE, CED, DCE, DEC, ECD, EDC CU St

An electronics store receives a shipment of 20 graphing calculators, including 5 that are defective. Four of the calculators are selected to be sent to a local high school. How many of these selections will contain no defective calculators? The number of ways to choose all selections that contain no defective calculators is

In the 6/52 lottery game, a player picks six numbers from 1 to 52. How many different choices does the player have if repetition is not allowed? Note that the order of the numbers is not important. Your answer is:

You want to do a survey of members of the junior class at Onslow High School in North Carolina. You want the sample to be a simple random sample. Your goal is to include 60 students in your sample. Which of the following scenarios below will generate a simple random sample? Assuming that the students are randomly assigned to classes, you put all the classes that contain juniors in them in a hat. You pick two classes from the hat and survey every junior from those two classes. Gather a list of all of the juniors. Select the first 30 females and the first 30 males on the list. Select the first 60 juniors that pass through the cafeteria door at lunch. Write the name of each student in the junior class on a slip of paper and put the papers in a hat. Mix the hat up. Randomly select 60 slips of paper from the container.

In how many ways could a club select two members, one to open their next meeting and one to close it, given that Alan will not be present? N=(James, Sandy, Jane, Alan, Tammy, Cathy, David, Sandy, Ashley} ways

Counting numbers are to be formed using only the digits 7, 8, and 9. Determine the number of different possibilities for the type of number described below. Four-digit numbers with one pair of adjacent 8s and no other repeated digits (Hint: You may want to split the task of designing such a number into three parts, such as (1) position the pair of 8s, (2) position the 7, and (3) position the 9.) The number of different possibilities for this type of number is (Type a whole number.) *****

In a window display at a flower shop, there are 3 spots for 1 plant each. To fill these 3 spots, Adam has 9 plants to select from, each of a different type. Selecting from the 9 plants, Adam can make how many possible display arrangements with 1 plant in each spot? (Note: The positions of the unselected plants do not matter.) F. 504 G. 729 H. 84 J. 55 K. 905

C) A TEACHER DECIDES TO GIVE SIX IDENTICAL PRIZES TO 6 OF THE 20 STUDENTS IN HIS CLASS. IN HOW MANY WAYS CAN THIS BE DONE? D) HOW MANY DISTINCT ARRANGEMENTS CAN BE MADE WITH THE LETTERS IN THE WORD CONNECTION?

A jar contains 69 jelly beans: 19 lemon, 15 watermelon, 15 blueberry, and 20 grape. Suppose that two jelly beans are randomly selected in succession without replacement (because you are eating them as you go). Find the probability of selecting two blueberry jelly beans. Enter a reduced fraction.

2. One apartment complex offers apartments with four different options, designated by A through D. A one bedroom two bedrooms three bedrooms four bedrooms B one bathroom two bathrooms C first floor second floor D lake view golf course view no special view How many apartment options are available?

One hundred sixty-five people each purchased one raffle ticket. Three winning tickets are randomly selected. If the first prize is $500, the second prize is $300, and the third prize is $100, in how many different ways can the prizes be awarded?

For her show "Outfront," Alicia can air 2 segments. If she has 14 segments to select from, in how many ways can she arrange the segments for her show?