Resources

Resources

Combinations and permutations

Sample question

2

: degree of difficulty low

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\begin{tabular}{lrlllll}

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5

50

20

200

170

1700

?

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You are at a sandwich shop. You can choose from white or rye bread, turkey or ham, and Swiss or American cheese to make your sandwich. All eight possible sandwich combinations are listed below. If we take sandwiches and as a subset of the sample space, which of the statements below describe this subset?

Hamid is playing a trivia game with multiple choice questions. Each question has

2

correct answers among

5

answer choices.

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Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random.

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What is the probability that Hamid guesses both answers correctly?

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Round your answer to two decimal places.

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\square

3

batches of cookies with

c

cookies in each batch. She then ate

8

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How many cookies does Anna have left?

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Write your answer as an expression.

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\square

\text{cookies}

complete the division problem using partial quotients.

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8,235 \div 5=

Nayara wants to know the percentage of each grade level of students at her school who drive to school. She has

4

grade levels in her school.

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Which of the following survey methods will allow Nayara to make a valid conclusion about what percentage of each grade level of students drive to school?

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1

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(A) Randomly select

48

students who drive to school and ask them their grade level.

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(B) Randomly select

12

students from each grade level and ask whether they drive to school.

The library is trying to decide which book to feature in next month's young adult book club, Salt to the Sea or The Sun is Also a Star.

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Which of the following survey methods will allow the library to make a valid conclusion about which book the young adults who use their library would prefer?

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1

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120

randomly selected people from a list of all young adults registered to the library.

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120

randomly selected people from a list of all people registered to the library.

City Councilwoman Kelly wants to know whether the residents of her district support a proposed school redistricting plan.

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Which of the following survey methods will allow Councilwoman Kelly to make a valid conclusion about whether residents of her district support the proposed plan?

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1

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200

residents of her district whose names are chosen at random.

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200

parents at the local playground.

Bella wants to conduct a survey to determine how many of the residents of Forks believe in supernatural creatures.

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Which of the following survey methods will allow Bella to make a valid conclusion about the percentage of residents of Forks that believe in supernatural creatures?

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1

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(A) Ask a randomly selected sample of residents to answer the question anonymously.

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(B) Ask a randomly selected sample of high school students to answer the question anonymously.

Rapunzel is looking at a plane flying in the sky. She is looking up at an angle of elevation of

36^{\circ}

. The horizontal distance from Rapunzel to the plane is

11

600

feet. How high above the ground is the plane?

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Note: Figure may not be drawn to scale.

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Provide an answer accurate to the nearest tenth.

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You're having dinner at a restaurant that serves

5

kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in

4

different flavors (tomato sauce, cheese sauce, meat sauce, and olive oil).

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If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with bow ties, cheese sauce, or both?

Every attendant at a town's Chili Cook-off received a raffle ticket. There were

8

raffle prizes, including

6

that were gift certificates to restaurants.

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4

prizes were randomly raffled away in the first hour of the cook-off, what is the probability that all of them are gift certificates to restaurants?

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Write your answer as a decimal rounded to four decimal places.._________

Chef Lloyd's fridge is filled with

7

5

of which contain whole milk. Before he begins to bake, he examines the cartons' expiration dates. If Chef Lloyd checks the expiration dates on

4

randomly selected cartons, what is the probability that all of them contain whole milk?

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Write your answer as a decimal rounded to four decimal places.._________

Mr. Shen brought in

8

solid colored eggs for his Physics classes.

5

of the eggs were blue. If Mr. Shen randomly chose

4

eggs for his first class to use in an egg drop experiment, what is the probability that all of them are blue? Write your answer as a decimal rounded to four decimal places.._________

Every attendant at a town's Chili Cook-off received a raffle ticket. There were

8

raffle prizes, including

5

that were cooking utensils. If

4

prizes were randomly raffled away in the first hour of the cook-off, what is the probability that all of them are cooking utensils?

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Write your answer as a decimal rounded to four decimal places.._________

Audrey and her best friend wanted to paint their apartment. In their storage closet, they found

8

cans of paint. Audrey remembered that

5

of the cans contained beige paint, but none of the cans had labels.

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If Audrey randomly opened

4

cans, what is the probability that all of them contain beige paint?

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Write your answer as a decimal rounded to four decimal places.

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Lucy and her dad went ice-fishing this winter. They caught

8

total fish, including

6

arctic char. If on the last day of the trip, Lucy randomly selected

4

fish to donate to fishermen who hadn't caught any fish that day, what is the probability that all of them are arctic char?

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Write your answer as a decimal rounded to four decimal places.______

An English teacher gave his class a choice of

8

6

of which are contemporary novels. If a student randomly picks

5

books, what is the probability that all of them are contemporary novels?

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Write your answer as a decimal rounded to four decimal places.___

Annie and her best friend wanted to paint their apartment. In their storage closet, they found

8

cans of paint. Annie remembered that

6

of the cans contained beige paint, but none of the cans had labels.

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If Annie randomly opened

5

cans, what is the probability that all of them contain beige paint?

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Write your answer as a decimal rounded to four decimal places.

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As Student Council President, Marcy organized a school-wide scavenger hunt. She hid

8

6

of which were hidden in the main office. If

5

goody bags were randomly discovered during first period, what is the probability that all of them were hidden in the main office?

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Write your answer as a decimal rounded to four decimal places._____

9

exercises over the span of a week.

7

of his exercises involve biking.

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If he randomly chose

6

exercises to do on Monday, what is the probability that all of them involve biking?

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Write your answer as a decimal rounded to four decimal places.

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An English teacher gave his class a choice of

8

6

of which are contemporary novels. If a student randomly picks

4

books, what is the probability that all of them are contemporary novels? Write your answer as a decimal rounded to four decimal places. ____

Erica and her stepmother wanted to start volunteering together. They found

7

opportunities online,

5

of which involved working with the elderly.

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If they randomly chose to apply to

4

of the opportunities, what is the probability that all of them involve working with the elderly?

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Write your answer as a decimal rounded to four decimal places.

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Tucker is filling out summer job applications, so that he can earn money to buy a car. Of the

9

jobs he's applying for,

7

are tutoring jobs.

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If Tucker randomly picks

6

applications to submit today, what is the probability that all of them are for tutoring jobs?

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Write your answer as a decimal rounded to four decimal places.

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7

5

of which are blue.

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If John randomly picks

4

buttons, what is the probability that all of them are blue?

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Write your answer as a decimal rounded to four decimal places.

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Mr. Lynch brought in

8

solid colored eggs for his Physics classes.

6

of the eggs were green. If Mr. Lynch randomly chose

5

eggs for his first class to use in an egg drop experiment, what is the probability that all of them are green?

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Write your answer as a decimal rounded to four decimal places.._________

9

seeds in order to plant an herb garden for her grandma. Of the seeds she bought,

7

were dill seeds.

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If Erin chooses to plant

6

random seeds on the east side of the garden, what is the probability that all of them are dill seeds?

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Write your answer as a decimal rounded to four decimal places.

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After touring a coffee bean farm, Lily impulsively bought

8

bags of coffee beans. Of the bags she bought,

6

were filled with caramel flavored coffee beans.

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If Lily randomly selects

5

of the bags to send to family members, what is the probability that all of them are caramel flavored?

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Write your answer as a decimal rounded to four decimal places.

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Brenna is handing out

8

invitations to her New Year's Eve party,

5

of which are printed on green paper. If Brenna randomly hands out

4

invitations before lunch, what is the probability that all of them are printed on green paper?

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Write your answer as a decimal rounded to four decimal places.._________

Kelly teaches a ceramics class on the weekends. In Sunday's class, the students created

8

6

of which were plates. After each class, Kelly bakes the clay objects in a hot kiln to harden them. Students pick up their finished pieces later in the week.

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If Kelly randomly chose

5

clay objects to bake in the kiln Sunday night, what is the probability that all of them are plates?

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Write your answer as a decimal rounded to four decimal places.

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The Danville High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were

8

6

of the bottles contained green soap.

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If a club member randomly selects

5

bottles to pour into the first soap bucket, what is the probability that all of them contain green soap?

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Write your answer as a decimal rounded to four decimal places.._________

Dana is shopping for a costume at a thrift store. There are

8

costumes hanging on the rack, including

6

food-shaped costumes. If the costumes all look like the right size, and Dana randomly selects

5

to try on, what is the probability that all of them are food-shaped costumes? Write your answer as a decimal rounded to four decimal places.._________

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Solve the right triangle.

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Round your answers to the nearest tenth.

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84

kids, three-sevenths bought their lunches. Of those who bought their lunches,

9

got a slice of pizza. What fraction of the students who bought their lunches got a slice of pizza? Write your fraction in simplest form.

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Matthew is saving money each week. Matthew's savings are represented by the table belor Find the rate of change.

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Matthew's Savings

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\begin{tabular}{|c|c|}

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(x)

& Total Savings

(y)

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3

\$ 82

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5

\$ 122

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7

\$ 162

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9

\$ 202

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1

2

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\$

\square

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Google Classroom

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Water is drained out of a tank at a rate of

r(t)=20 e^{-0,1 t^{2}}

liters per minute, where

t

is the time in minutes,

0 \leq t \leq 10

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How much water is drained between times

t=3

t=9

minutes? Use a graphing calculator and round your answer to three decimal places.

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Report a problem

2 / 40

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0

25

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Emily volunteers on the weekend at the Central Library. As a school oroject, she decides to record how many people visit the library, and where they go. On Saturday,

416

people went to The Youth Wing,

448

seople went to Social Issues, and

341

went to Fiction and Literature.

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On Sunday, the library had

500

total visitors. Based on what Emily had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.

Zachary has a bag that contains strawberry chews, cherry chews, and peach chews. He performs an experiment. Zachary randomly removes a chew from the bag, records the result, and returns the chew to the bag. Zachary performs the experiment

66

times. The results are shown below:

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A strawberry chew was selected

61

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A cherry chew was selected

3

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A peach chew was selected

2

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If the experiment is repeated

200

more times, about how many times would you expect Zachary to remove a peach chew from the bag? Round your answer to the nearest whole number.

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984 \div 10

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1 / 3

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A group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by those who did or did not eat breakfast in the following table. Determine whether eating breakfast and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth

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\begin{tabular}{|c|c|c|}

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\hline & Passed & Failed \\

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\hline Did Eat Breakfast &

38

19

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\hline Didn't Eat Breakfast &

58

29

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1

2

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\mathrm{P}(

did eat breakfast

) \times \mathrm{P}(

)=\square

\mathrm{P}(

did eat breakfast and pass

)=\square

, the two results are so the events are

Each page of a top-secret report on aliens requires

2 \mathrm{~KB}

of space in digital format.

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What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds

4 \cdot 10^{6} \mathrm{~KB}

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Write your answer in scientific notation, and round to one decimal place.

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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

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452,443,434, \ldots

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32

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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

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461,452,443, \ldots

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39

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3-2

Factor the expression completely.

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9 x-24

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Convert the decimal below to a fraction in simplest form.

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0.827

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Convert the decimal below to a fraction in simplest form.

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0.427

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Ramkin is going to flip a fair coin

1200

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What is the best prediction for the number of times that the coin will land heads up?

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1

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50

\newline

50

times but probably not exactly

50

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600

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600

times but probably not exactly

600

Mekala has an MP

3

player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has

4

2

country songs, and

3

jazz songs on it. Mekala plans to listen to

270

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Complete the following statement with the best prediction.

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Mekala will listen to...

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1

\newline

60

\newline

60

country songs but probably not exactly

60

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210

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210

country songs but probably not exactly

210

Shun is going to flip a fair coin

450

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Complete the following statement with the best prediction.

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The coin will land tails up...

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1

\newline

175

\newline

175

times but probably not exactly

175

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225

\newline

225

times but probably not exactly

225