Permutations and Combinations Questions and Answers

All Harold's ties are red except for two. All Harold's ties are blue except for two. All Harold's ties are brown except for two. How many ties does Harold have? Harold has red tie(s), blue tie(s), and brown tie(s).

A combination lock will open when the right choice of three numbers (from 1 to 35) is selected. How many different lock combinations are possible? 128,625 42,875 1225 35 105

There are 14 members of the scholastic bowl team, 8 of whom are boys and 6 of whom are girls. The coach wants to play 3 boys and 1 girl in the next round. How many different teams of 3 boys and 1 girl could be formed to play the next round?

A state makes auto license plates that have two letters (excluding I, O, and Q) followed by four digits of which the first digit is not zero. How many different license plates are possible? 3,085,128 3,470,769 O4,761,000

You need to arrange seven of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you? ways (Type a whole number.)

An investor will randomly select 6 stocks from 20 for an investment. How many combinations are possible?

Knowledge: 1. A coin is tossed three times. What is the best description of the tree diagram that illustrates this event? A 2 stages, 3 branches per stage, 6 outcomes B 3 stages, 2 branches per stage, 8 outcomes C 2 stages, 3 branches per stage, 9 outcomes D 3 stages, 2 branches per stage, 6 outcomes 2. Cameron is forming a password containing 3 characters. He has decided that the first character will be a capital letter and the last character will be a digit. All other characters will be lower case letters. How many unique passwords could Cameron form? A 39 B 780 C 4056000 D 6760 D 6760

Cameron is forming a password containing 3 characters. He has decided that the first character will be a capital letter and the last character will be a digit. All other characters will be lower case letters. How many unique passwords could Cameron form? A 39 B 780 C 4056000 D 6760

If the word PERMUTE is permuted in all possible ways and the different resulting words are written down in alphabetical order (also known as dictionary order), irrespective of whether the word has meaning or not, then the 720th word would be: (A) EEMPRTU (B) EUTRPME (C) UTRPMEE (D) MEETPUR.

The 13 players on a volleyball team are to line up for a team photograph. The seven shortest players will be in the front row. The remaining players will be in the back row. The coach will be in the back row on either the left or right end or in the middle. How many different arrangements are there for the team photo?

The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are twelve entries in the trifecta race, how many tickets must you purchase to guarantee a win?

A typical Chinese restaurant will often feature a Special Dinner, in which the customer has the choice of ordering one appetizer and one entree. 1. If there are 8 appetizers and 11 entrees, how many different Special Dinners are there? 2. If there are 12 appetizers and 7 entrees, how many different Special Dinners are there? 3. There are 12 appetizers; 4 are soups, 6 contain meat, and 2 do not. In how many different orders can 3 different appetizers be brought to the table? 4. In how many different orders can 5 different appetizers of the 12 be brought to the table? 5. Do Exercises 3-4 involve permutations or combinations?

Use: Ck n n! k! (n-k)! to solve the combination. How many different combinations of six people can sit in four chairs? Assume one person sits in each chair. [?] ways

As part of a quality-control program, 3 light bulbs from each batch of 100 are tested. In how many ways can this test batch be chosen? Note: nCr =n!/ r!n-r)!

In how many ways can a password be made using 4 letters from the 26 letter English alphabet, if letters cannot be repeated? [?] ways Note: nPr = n! / (n-r)!

Suppose you choose four books to read from a summer reading list of 12 books. How many different combinations of books are possible?

In how many ways can a person select 3 golf shirts for vacation from a selection of 10 golf shirts?

A superintendent has 12 schools under his jurisdiction. If he randomly selects 3 schools from these 12, how many different combinations are possible?

For a class, Mrs. Hawk brought in 7 different packages of colored pens. The teacher randomly selects 2 packages. How many different combinations are there?

An environmental agency will randomly select 4 houses from a block containing 25 houses for a radon check. How many different combinations are possible?

In how many ways can first, second, and third prizes be awarded in a contest with 130 contestants?

Suppose a designer has a palette of 16 colors to work with, and wants to design a flag with 3 vertical stripes, all of different colors. How many possible flags can be created?

A restaurant offers a $12 dinner special that has 5 choices for an appetizer, 13 choices for an entrée, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?

For the jumble puzzle VOBAE, complete the parts below. a) Determine the number of possible arrangements of the letters given. b) What is the word when the letters are placed in the proper order? a) There are possible arrangements.

A pea plant must have exactly one of each of the following pairs of traits: short (s) or tall (t) and white (wh) or purple (p) flowers (for example, short with white flowers). (a) How many different classifications of pea plants are possible? There are 16 classifications.

If you place these marbles in a bag, close your eyes, and choose a marble, what is the probability that it will be yellow?

Kristin Wilson lives in Anderson, South Carolina, and wishes to visit relatives in the following South Carolina cities: Columbia, Rock Hill, Sumter, Greenville, and Florence. In how many ways can she visit each of these cities and return to her home in Anderson? There are___different ways that Kristin can visit each city and return home.

In an examination, 5 children were found to have their mobiles in their pocket. The invigilator fired them and took their mobiles in his possession towards the end of the test, Invigilator randomly returned their mobiles. The number of ways in which atmost two children did not get their own mobiles is 11 λ then λ =

A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 12 choices for an entrée, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert? A meal can be chosen in ways. (Type a whole number.)

A license plate is to consist of 3 letters followed by 2 digits. Determine the number of different license plates possible if the first letter must be an A, E, I, O, U or Y and repetition of letters and numbers is not permitted. 405,600 324,000 342,000 205,200

For her birthday party, Jessica's father will let her choose one style of birthday cake, 1 kind of pizza, and 1 flavor of drink. There are 5 cake styles, 7 kinds of pizza, and 4 drink flavors to choose from. How many different ways can Jessica choose these items for her party? A. 140 B. 70 C. 35 D. 20

Which of the following describes a permutation? A. The boss selected 5 workers to be on a planning committee. B. A teacher arranged 5 students in a row from shortest to tallest. C. George ordered 5 toppings to put on a supreme pizza. D. Anna chose 5 sweaters from her closet to donate to charity.

A jar has two red, three blue, one white, and three yellow jelly beans. How many ways are there to line up the jelly beans? 5,040 20,160 60,480 362,880

How many different 10-letter words (real or imaginary) can be formed from the following letters? K, G, C, I, A, A, G, M, X, T ten-letter words (real or imaginary) can be formed with the given letters. (Type a whole number.)

A certain lottery has 30 numbers. In how many different ways can 5 of the numbers be selected? (Assume that order of selection is not important.) There are different ways the numbers can be selected. (Simplify your answer.)

A basketball team has ten players. Each day at practice, one is chosen to bring out the basketballs and another is chosen to return the basketballs to the storage closet. What is the chance that Demetrius will bring out the basketballs and Sam will return the basketballs to the storage closet for thirty practices in a row?

The dog has a litter of eight puppies. Your dad wants to sell three of them. How many ways can he make the group of three to sell? 8 4 56 336

Due to the many cell phones in use, there is increasingly a shortage of telephone numbers. To alleviate the problem, the government agency that oversees phone numbers and area codes needs to determine a new area code. How many area codes can be made? (Assume that an area code consists of three digits and it cannot start with zero as the only restriction.) 1,000 995 800 900

Twelve contestants are competing in a talent show. Which of the following represents the possible outcomes if there can be only one recipient for first, second, and third place? \(3!\) \(12!\) 12³ 12.11.10

Isaiah's Ice Cream Shoppe allows customers to choose 5 toppings for their famous sundaes. There are 12 different toppings from which customers can choose. How many different combinations of 5 toppings can be made from the 12 options? 60 792 95,040 50,400

Paul has four shirts, two ties, and three pairs of pants. How many possible outfits can he make if he chooses one Item from each group? 504 84 12 24

Mr. Kranz wants to buy a new car. He is considering a compact car, full-size sedan, or a sports utility vehicle. He can choose a standard or a luxury model for all three types of cars. There are blue, silver, and white colors available to choose from for each model. How many possible choices does Mr. Kranz have? 56 336 9 18

A credit card account number has sixteen digits where each digit is a selected from a set of numbers from 0-9. Which of the following represents the total number of possible credit card accounts?

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

A school editor Is choosing three of eight seniors and two of six juniors to report on graduation. What is the number of possible ways for the school editor to choose the team of reporters? 336 450 840 1,680

To pack for a business trip, Steve chooses four of nine dress shirts and two of three blazers. What is the possible number of ways for Steve to pack for his trip? 3 126 378 3,204

There are eight fiction books and seven nonfiction books on a shelf. Sara wants to bring three fiction and two nonfiction books on vacation, and she is going to read them in the order she chooses. What is the possible number of different ways for Sara to choose the books for vacation? 21 56 1,176 14,112

A credit card has a four-digit pin number consisting of four different digits from 0-9. How many possible pin numbers are there? 720 5,040 151,200 1,000,000

Your little brother asks you to help him with his dinosaur project for school. He has narrowed his list down to 10 of his favorite dinosaurs, but he can only choose 3 of them for his project. How many ways can he choose 3 dinosaurs on his project? 3 10 720 120

Identify the event that is a combination. A baseball manager choosing a first and second batter from nine starters. The order of placing seven books on a shelf. A person selecting four balls without replacement from a container of twenty balls. The number of four-digit passcodes with no digits repeated.