In how many ways can the first five letters of the alphabet be arranged if each letter is used only once?

26 x 26 x 26 x 26 x 26 = 11881376

How many license plates consisting of three letters followed by three numbers are possible when no repetition is allowed?

26 x 25 x 24 x 10 x 9 x 8 = 11232000

26 x 26 x 26 x 10 x 10 x 10 = 17576000

26 x 25 x 24 x 9 x 8 x 7 = 7862400

26 x 26 x 26 x 9 x 9 x 9 = 12812904

You go to an entertainment center and get to pick how to spend the day with friends: (activity 1: go-karts, bowling, mini golf), (food: hot dogs, corn dogs, hamburgers, pizza), and (activity 2: laser tag, arcade, skating). What is the probability of selecting to go-kart, eat ANY of the four food options, and ending the day with laser tag? (Hint: Remember to calculate a probability find the number of ways to get what you want divided by the total number of options.)

4 36 = 1 9 \frac{4}{36}=\frac{1}{9} 3 6 4 = 9 1

6 36 = 1 6 \frac{6}{36}=\frac{1}{6} 3 6 6 = 6 1

4 80 = 1 20 \frac{4}{80}=\frac{1}{20} 8 0 4 = 2 0 1

You go to an ice cream shop and get to choose: (flavor: Chocolate, Vanilla, Strawberry, Swirl), (scoops: 1, 2, or 3), (toppings: Sprinkles, Gummi Bears, Nerds, Chocolate Chips), and (cone: Waffle or Sugar). What is the probability of buying a Swirl, Two-scoop ice cream with Chocolate Chips on a Waffle Cone? (Hint: To find a probability, find the number of ways to get what you want divided by the total number of options.)

4 96 = 1 24 \frac{4}{96}=\ \frac{1}{24} 9 6 4 = 2 4 1

4 16 = 1 4 \frac{4}{16}=\frac{1}{4} 1 6 4 = 4 1

The Fundamental Counting Principle (also called the Counting Principle) helps us find the total number of ways to satisfy two (or more) different independent conditions. To use it we

multiply the number of options in each category.

multiply the options in the categories by 2.

add all the options in the categories together.

add the number of options in each category.

Fundamental Counting Principle

Authored by Cheryl Askay

Mathematics

8th - 11th Grade

CCSS covered

Used 30+ times

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

22 questions

Show all answers

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The tree diagram shows the outcomes of rolling a die and flipping a coin.
How many total outcomes are there?

Tags

CCSS.HSS.CP.B.9

CCSS.HSS.CP.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Which of the following situations is represented by this tree diagram?

3 shirt options, 6 pants options, and 12 shoe options

3 shirt options, 2 pants options, and 2 shoe options

2 shirt options, 3 pants options, and 1 shoe option

Tags

CCSS.7.EE.B.3

CCSS.3.OA.D.8

CCSS.4.OA.A.3

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Tree Diagram

A written list of all possible outcomes

A description of all possible outcomes

A drawing with branches of all possible outcomes

Tags

CCSS.7.SP.C.8

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The cafeteria is serving three kinds of sandwiches: tuna (T), chicken, (C), and peanut butter (P). They are also serving a choice of two drinks: milk (M) or water (W). Which shows the complete set of possible combinations?

TW, CW, PW

TW, TM, TC, CW, PW

TW, TM, CW, CM, PW, PM

TCP, MW

Tags

CCSS.3.OA.A.3

CCSS.3.OA.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

If you draw a random card from a standard deck of cards, how many possible outcomes?

Tags

CCSS.HSS.CP.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream. A customer gets to choose a cone and a type of ice cream. How many events are described here?

Tags

CCSS.3.OA.A.3

CCSS.3.OA.A.1

CCSS.3.OA.C.7

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

7 because 2 + 3 + 2

12 because 2 x 3 x 2

Tags

CCSS.7.EE.B.3

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

20 questions

Penilaian Harian Ke- 1 Materi Bilangan Berpangkat dan Bentuk Akar

Quiz

•

9th Grade

20 questions

Factorización: Trinomio x^2+bx+c

Quiz

•

9th Grade

20 questions

LATIHAN SOAL 1

Quiz

•

9th Grade

20 questions

1.0 INDEKS Tingkatan 3

Quiz

•

KG - Professional Dev...

20 questions

Suites arithmetiques et sommes

Quiz

•

11th - 12th Grade

18 questions

Teza clasa a VII-a sem.II

Quiz

•

7th - 8th Grade

17 questions

Применение производной

Quiz

•

1st - 10th Grade

20 questions

Simpanan dan Pelaburan

Quiz

•

7th - 9th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

10 questions

Probability Practice

Quiz

•

4th Grade

15 questions

Probability on Number LIne

Quiz

•

4th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

6 questions

Appropriate Chromebook Usage

Lesson

•

7th Grade

10 questions

Greek Bases tele and phon

Quiz

•

6th - 8th Grade

Discover more resources for Mathematics

23 questions

TSI Math Vocabulary

Quiz

•

10th - 12th Grade

15 questions

Graphing Inequalities

Quiz

•

7th - 9th Grade

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

8 questions

8th U5L20 Volume of Sphere

Quiz

•

8th Grade

20 questions

Solving Systems of Equations Review

Quiz

•

8th Grade

20 questions

Slope from a Graph

Quiz

•

8th Grade

15 questions

Combine Like Terms and Distributive Property

Quiz

•

8th - 9th Grade

10 questions

Plotting Points on a Coordinate Plane: Quadrant 1 Essentials

Interactive video

•

6th - 10th Grade

Fundamental Counting Principle

The tree diagram shows the outcomes of rolling a die and flipping a coin.
How many total outcomes are there?

Which of the following situations is represented by this tree diagram?

Tree Diagram

The cafeteria is serving three kinds of sandwiches: tuna (T), chicken, (C), and peanut butter (P). They are also serving a choice of two drinks: milk (M) or water (W). Which shows the complete set of possible combinations?

If you draw a random card from a standard deck of cards, how many possible outcomes?

An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream. A customer gets to choose a cone and a type of ice cream. How many events are described here?

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

Three students are scheduled to give oral reports on Monday. In how many ways can their presentations be ordered?

In how many ways can the first five letters of the alphabet be arranged if each letter is used only once?

The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many passwords are possible if letters can be repeated?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Fundamental Counting Principle

The tree diagram shows the outcomes of rolling a die and flipping a coin. How many total outcomes are there?

Which of the following situations is represented by this tree diagram?

Tree Diagram

The cafeteria is serving three kinds of sandwiches: tuna (T), chicken, (C), and peanut butter (P). They are also serving a choice of two drinks: milk (M) or water (W). Which shows the complete set of possible combinations?

If you draw a random card from a standard deck of cards, how many possible outcomes?

An ice cream shop offers a choice of three types of cones and 31 flavors of ice cream. A customer gets to choose a cone and a type of ice cream. How many events are described here?

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

Three students are scheduled to give oral reports on Monday. In how many ways can their presentations be ordered?

In how many ways can the first five letters of the alphabet be arranged if each letter is used only once?

The letters A, B, C, and D are used to form four-letter passwords for entering a computer file. How many passwords are possible if letters can be repeated?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

The tree diagram shows the outcomes of rolling a die and flipping a coin.
How many total outcomes are there?