Fundamental Counting Principle Beginner-Intermediate Worksheet: Focus on common variations practice Fundamental Counting Principle BEGINNER INTERMEDIATE

Level up your Fundamental Counting Principle skills! You're at Worksheet 4 of 10 (33% through this series). This step-up challenge worksheet features 20 beginner-intermediate-level problems with a focus on common variations practice. Topics covered: fundamental counting principle for competitive exams, how to solve fundamental counting principle, fundamental counting principle tricks.

📝 Worksheet 4 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner Intermediate level

What you'll learn in this worksheet:

Understand the logic behind how to solve fundamental counting principle
Learn step-by-step approaches to common variations practice
Bridge the gap between basic and advanced concepts
Handle problems with increasing complexity
Master fundamental counting principle for competitive exams through focused practice

Your progress through Fundamental Counting Principle

Worksheet 4 of 10 (33% complete)

Question 1

A restaurant offers 5 appetizers, 6 main courses, and 5 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 5 options
- Second choice: 6 options
- Third choice: 5 options

Calculation:
Total ways = 5 × 6 × 5 = 150

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 5 first choices can be paired with each of the 6 second choices (5×6=30), and each of these can be combined with any of the 5 third choices.

Question 2

A restaurant offers 3 appetizers, 7 main courses, and 3 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 7 options
- Third choice: 3 options

Calculation:
Total ways = 3 × 7 × 3 = 63

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 7 second choices (3×7=21), and each of these can be combined with any of the 3 third choices.

Question 3

A car model has 6 colors, 5 engine types, and 3 interior options. How many different different car configurations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 6 options
- Second choice: 5 options
- Third choice: 3 options

Calculation:
Total ways = 6 × 5 × 3 = 90

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 6 first choices can be paired with each of the 5 second choices (6×5=30), and each of these can be combined with any of the 3 third choices.

Question 4

A restaurant offers 4 appetizers, 5 main courses, and 4 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 4 options
- Second choice: 5 options
- Third choice: 4 options

Calculation:
Total ways = 4 × 5 × 4 = 80

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 4 first choices can be paired with each of the 5 second choices (4×5=20), and each of these can be combined with any of the 4 third choices.

Question 5

A car model has 5 colors, 6 engine types, and 3 interior options. How many different different car configurations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 5 options
- Second choice: 6 options
- Third choice: 3 options

Calculation:
Total ways = 5 × 6 × 3 = 90

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 5 first choices can be paired with each of the 6 second choices (5×6=30), and each of these can be combined with any of the 3 third choices.

Question 6

A restaurant offers 4 appetizers, 7 main courses, and 2 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 4 options
- Second choice: 7 options
- Third choice: 2 options

Calculation:
Total ways = 4 × 7 × 2 = 56

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 4 first choices can be paired with each of the 7 second choices (4×7=28), and each of these can be combined with any of the 2 third choices.

Question 7

A restaurant offers 3 appetizers, 4 main courses, and 3 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 4 options
- Third choice: 3 options

Calculation:
Total ways = 3 × 4 × 3 = 36

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 4 second choices (3×4=12), and each of these can be combined with any of the 3 third choices.

Question 8

A car model has 3 colors, 5 engine types, and 5 interior options. How many different different car configurations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 5 options
- Third choice: 5 options

Calculation:
Total ways = 3 × 5 × 5 = 75

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 5 second choices (3×5=15), and each of these can be combined with any of the 5 third choices.

Question 9

A student has 3 shirts, 7 pants, and 4 pairs of shoes. How many different outfits can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 7 options
- Third choice: 4 options

Calculation:
Total ways = 3 × 7 × 4 = 84

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 7 second choices (3×7=21), and each of these can be combined with any of the 4 third choices.

Question 10

A car model has 4 colors, 4 engine types, and 5 interior options. How many different different car configurations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 4 options
- Second choice: 4 options
- Third choice: 5 options

Calculation:
Total ways = 4 × 4 × 5 = 80

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 4 first choices can be paired with each of the 4 second choices (4×4=16), and each of these can be combined with any of the 5 third choices.

Question 11

A restaurant offers 3 appetizers, 5 main courses, and 2 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 5 options
- Third choice: 2 options

Calculation:
Total ways = 3 × 5 × 2 = 30

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 5 second choices (3×5=15), and each of these can be combined with any of the 2 third choices.

Question 12

A restaurant offers 5 appetizers, 6 main courses, and 3 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 5 options
- Second choice: 6 options
- Third choice: 3 options

Calculation:
Total ways = 5 × 6 × 3 = 90

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 5 first choices can be paired with each of the 6 second choices (5×6=30), and each of these can be combined with any of the 3 third choices.

Question 13

A restaurant offers 5 appetizers, 6 main courses, and 3 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 5 options
- Second choice: 6 options
- Third choice: 3 options

Calculation:
Total ways = 5 × 6 × 3 = 90

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 5 first choices can be paired with each of the 6 second choices (5×6=30), and each of these can be combined with any of the 3 third choices.

Question 14

A restaurant offers 6 appetizers, 4 main courses, and 2 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 6 options
- Second choice: 4 options
- Third choice: 2 options

Calculation:
Total ways = 6 × 4 × 2 = 48

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 6 first choices can be paired with each of the 4 second choices (6×4=24), and each of these can be combined with any of the 2 third choices.

Question 15

A student has 3 shirts, 5 pants, and 5 pairs of shoes. How many different outfits can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 5 options
- Third choice: 5 options

Calculation:
Total ways = 3 × 5 × 5 = 75

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 5 second choices (3×5=15), and each of these can be combined with any of the 5 third choices.

Question 16

A car model has 4 colors, 5 engine types, and 4 interior options. How many different different car configurations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 4 options
- Second choice: 5 options
- Third choice: 4 options

Calculation:
Total ways = 4 × 5 × 4 = 80

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 4 first choices can be paired with each of the 5 second choices (4×5=20), and each of these can be combined with any of the 4 third choices.

Question 17

A student has 3 shirts, 7 pants, and 4 pairs of shoes. How many different outfits can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 7 options
- Third choice: 4 options

Calculation:
Total ways = 3 × 7 × 4 = 84

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 7 second choices (3×7=21), and each of these can be combined with any of the 4 third choices.

Question 18

A restaurant offers 4 appetizers, 4 main courses, and 4 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 4 options
- Second choice: 4 options
- Third choice: 4 options

Calculation:
Total ways = 4 × 4 × 4 = 64

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 4 first choices can be paired with each of the 4 second choices (4×4=16), and each of these can be combined with any of the 4 third choices.

Question 19

A restaurant offers 3 appetizers, 4 main courses, and 5 desserts. How many different meal combinations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 4 options
- Third choice: 5 options

Calculation:
Total ways = 3 × 4 × 5 = 60

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 4 second choices (3×4=12), and each of these can be combined with any of the 5 third choices.

Question 20

A car model has 3 colors, 6 engine types, and 5 interior options. How many different different car configurations can be made?

Step-by-Step Solution:

Concept: This problem uses the Fundamental Counting Principle (Multiplication Rule). When making sequential independent choices, multiply the number of options at each step.

Analysis:
- First choice: 3 options
- Second choice: 6 options
- Third choice: 5 options

Calculation:
Total ways = 3 × 6 × 5 = 90

Key Principle: For independent sequential events, multiply the number of choices at each stage.

Verification: Each of the 3 first choices can be paired with each of the 6 second choices (3×6=18), and each of these can be combined with any of the 5 third choices.

📝 Continue your Fundamental Counting Principle practice. Worksheet 4 focuses on common variations practice.

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