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Fundamental Counting Principle - Intermediate Level: tricky scenarios handling Fundamental Counting Principle INTERMEDIATE

This expert challenge 📈 worksheet focuses on Fundamental Counting Principle - a key topic in Permutation Combination. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve fundamental counting principle, fundamental counting principle tricks, and fundamental counting principle shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Fundamental Counting Principle
Worksheet 5 of 10 (44% complete)

Question 1

A car model has 5 colors, 7 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: 5 options
- Second choice: 7 options
- Third choice: 5 options

Calculation:
Total ways = 5 × 7 × 5 = 175

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 7 second choices (5×7=35), and each of these can be combined with any of the 5 third choices.

Question 2

A restaurant offers 5 appetizers, 7 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: 7 options
- Third choice: 5 options

Calculation:
Total ways = 5 × 7 × 5 = 175

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 7 second choices (5×7=35), and each of these can be combined with any of the 5 third choices.

Question 3

A car model has 5 colors, 6 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: 5 options
- Second choice: 6 options
- Third choice: 4 options

Calculation:
Total ways = 5 × 6 × 4 = 120

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 4 third choices.

Question 4

A student has 3 shirts, 4 pants, and 2 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: 4 options
- Third choice: 2 options

Calculation:
Total ways = 3 × 4 × 2 = 24

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 2 third choices.

Question 5

A car model has 3 colors, 6 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: 3 options
- Second choice: 6 options
- Third choice: 4 options

Calculation:
Total ways = 3 × 6 × 4 = 72

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 4 third choices.

Question 6

A student has 6 shirts, 5 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: 6 options
- Second choice: 5 options
- Third choice: 4 options

Calculation:
Total ways = 6 × 5 × 4 = 120

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 4 third choices.

Question 7

A restaurant offers 5 appetizers, 6 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: 5 options
- Second choice: 6 options
- Third choice: 2 options

Calculation:
Total ways = 5 × 6 × 2 = 60

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 2 third choices.

Question 8

A student has 6 shirts, 5 pants, and 3 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: 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 9

A student has 6 shirts, 6 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: 6 options
- Second choice: 6 options
- Third choice: 4 options

Calculation:
Total ways = 6 × 6 × 4 = 144

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 6 second choices (6×6=36), and each of these can be combined with any of the 4 third choices.

Question 10

A restaurant offers 6 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: 6 options
- Second choice: 6 options
- Third choice: 5 options

Calculation:
Total ways = 6 × 6 × 5 = 180

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 6 second choices (6×6=36), and each of these can be combined with any of the 5 third choices.

Question 11

A student has 4 shirts, 6 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: 4 options
- Second choice: 6 options
- Third choice: 5 options

Calculation:
Total ways = 4 × 6 × 5 = 120

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 6 second choices (4×6=24), and each of these can be combined with any of the 5 third choices.

Question 12

A student has 4 shirts, 6 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: 4 options
- Second choice: 6 options
- Third choice: 4 options

Calculation:
Total ways = 4 × 6 × 4 = 96

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 6 second choices (4×6=24), and each of these can be combined with any of the 4 third choices.

Question 13

A restaurant offers 5 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: 5 options
- Second choice: 4 options
- Third choice: 5 options

Calculation:
Total ways = 5 × 4 × 5 = 100

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

Question 14

A car model has 6 colors, 4 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: 4 options
- Third choice: 3 options

Calculation:
Total ways = 6 × 4 × 3 = 72

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 3 third choices.

Question 15

A car model has 3 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: 3 options
- Second choice: 6 options
- Third choice: 3 options

Calculation:
Total ways = 3 × 6 × 3 = 54

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 3 third choices.

Question 16

A restaurant offers 4 appetizers, 6 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: 6 options
- Third choice: 2 options

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

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

Question 17

A student has 4 shirts, 5 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: 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 18

A restaurant offers 3 appetizers, 5 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: 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 19

A car model has 5 colors, 4 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: 4 options
- Third choice: 3 options

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

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 4 second choices (5×4=20), and each of these can be combined with any of the 3 third choices.

Question 20

A car model has 5 colors, 4 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: 5 options
- Second choice: 4 options
- Third choice: 4 options

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

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