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Fundamental Counting Principle (pre) - Printable Mathematics Worksheets year 10 - Wayground

Fundamental Counting Principle (pre)

15 questions

9th - 12th Grade

Mathematics

Fundamental Counting Principle (pre) is a free printable mathematics worksheet for students in Grades 9–12. It contains 15 multiple-choice questions that build fluency with finding the total number of outcomes by multiplying the number of choices in each category. Students apply the principle to car selections, ice cream orders, entertainment plans, coin tosses, dice and coin combinations, meals, outfits, lunch combinations, passwords, license plates, and quiz responses. The worksheet also distinguishes situations in which repetition is allowed from those in which choices cannot repeat. This worksheet is useful for introducing or reviewing how the Fundamental Counting Principle models multi-step choices without listing every outcome. Students first identify the choices at each stage, then select or evaluate the corresponding multiplication expression, including cases such as four coin tosses, repeated password letters, and license plates with or without repetition. It is suitable for independent practice, class review, or a formative check, and includes a complete answer key for efficient grading.

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Fundamental Counting Principle (pre)

Total questions: 15

Name
Class
Date
1.

The Fundamental Counting Principle allows you to...

a)

see each and every possible outcome possibility in your sample.

b)

find the number of total outcomes in your sample.

c)

count how many times you must do a tree diagram.

d)

see how many outcomes will not show up on a tree diagram.

2.

Use the Fundamental Counting Principle to find out how many total outcomes you have:


You are buying a car and have to make the following decisions: (brand: Toyota, Honda, Ford), (color: Red, Green, Blue, Black, Silver), (transmission: Manual or Automatic)

a)

10

b)

3

c)

30

d)

72

3.

Use the Fundamental Counting Principle to find out how many total outcomes you have:


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).

a)

96

b)

4

c)

14

d)

240

4.

Use the Fundamental Counting Principle to find out how many total outcomes you have:


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)

a)

80

b)

10

c)

3

d)

36

5.

Use the Fundamental Counting Principle to find out how many total outcomes you have:


You toss 4 coins: (coin 1: H or T), (coin 2 : H or T), (coin 3 (H or T), and (coin 4: H or T)

a)

8

b)

81

c)

16

d)

4

6.

Use the Fundamental Counting Principle to find out how many total outcomes you have:


You roll 2 dice and flip 3 coins: (die 1: 1, 2, 3, 4, 5, 6), (die 2: 1, 2, 3, 4, 5, 6), (coin 1: H or T), (coin 2: H or T), and (coin 3: H or T)

a)

18

b)

288

c)

392

d)

5

7.

How do you do the Fundamental Counting Principle?

a)

You multiply the categories by 2.

b)

You add all the categories together.

c)

You add the number of options in each category.

d)

You multiply the number of options in each category.

8.

The Palace of Pizza offers small, medium, or large pizzas with 14 different toppings available. How many different 1-topping pizzas do they serve?

a)

3 x 14 = 42

b)

3 + 14 = 17

c)

14 x 14 x 14 = 2744

d)

14 x 13 x 12 = 2184

9.

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?

a)

4 x 4 x 4 x 4 = 256

b)

4 x 3 x 2 x 1 = 24

c)

4 + 4 + 4 + 4 = 16

d)

4 + 3 + 2 + 1 = 10

10.

A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each has a main dish, a salad, and a dessert?

a)

5 x 3 x 4 = 60

b)

5 + 3 + 4 = 12

11.

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

a)

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

b)

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

c)

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

d)

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

12.

How many license plate numbers consisting of three letters followed by three numbers are possible when repetition is allowed?

a)

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

b)

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

c)

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

d)

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

13.
How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?
a)
15
b)
40
c)
80
d)
10
14.

A menu has 6 different sandwiches, with 3 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad and beverage can be ordered?

a)
30
b)
17
c)
90
d)
270
15.

A seven-question quiz has 4 true/false questions followed by 3 multiple choice questions. For each multiple choice question there are four possible answers. In how many different ways is it possible to answer the seven questions?

a)

12

b)

80

c)

28

d)

1024

Answer Key

Fundamental Counting Principle (pre)

Total questions: 15

1.
b)

find the number of total outcomes in your sample.

2.
c)

30

3.
a)

96

4.
d)

36

5.
c)

16

6.
b)

288

7.
d)

You multiply the number of options in each category.

8.
a)

3 x 14 = 42

9.
a)

4 x 4 x 4 x 4 = 256

10.
a)

5 x 3 x 4 = 60

11.
a)

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

12.
a)

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

13.
c) 80
14.
d) 270
15.
d)

1024

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FAQs

What does this Fundamental Counting Principle worksheet help students learn?

This 15-question multiple-choice worksheet helps students calculate the total number of outcomes by multiplying the choices in each category. Students apply the rule to real-world combinations such as cars, meals, outfits, passwords, license plates, coin and dice results, and quiz answers. Several items specifically require students to recognize whether repetition is allowed, making the practice more precise than simply multiplying familiar numbers.

How can I use this worksheet to teach the Fundamental Counting Principle?

Introduce the worksheet by modeling one multi-category example, such as choosing a car brand, color, and transmission, and represent the total as 3 × 5 × 2. Ask students to explain why the choices are multiplied rather than added, then have them solve the remaining scenarios independently or in pairs. Use the password and license-plate questions for a follow-up discussion about how allowing or preventing repetition changes each factor.

What mistakes should I watch for when students complete this worksheet?

Students may add the numbers of choices instead of multiplying them, especially in the meal, outfit, and lunch-combination questions. They may also use the same factor in every position when repetition is not allowed, as in the three-letter, three-number license plate problem. Check that students count each coin and die separately in the probability-style items and distinguish four-choice multiple-choice questions from two-choice true/false questions in the final quiz item.

How do I assign and grade this Fundamental Counting Principle worksheet?

You can assign this worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format can also support classrooms that are reducing screen time while students practise counting outcomes.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the multi-step choices and answer options are easier to follow. You can also apply a dyslexia-friendly font or translate the worksheet into another language when helpful. These adjustments can make the calculation expressions and word-problem details clearer without changing the Fundamental Counting Principle practice.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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