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Master Fundamental Counting Principle - Intermediate-Advanced Level Problems Fundamental Counting Principle INTERMEDIATE ADVANCED

Excel in competitive exams with this self assessment worksheet on Fundamental Counting Principle. Worksheet 7 of 10 contains 20 intermediate-advanced-level problems. Target your accuracy improvement skills while practicing fundamental counting principle shortcut methods, fundamental counting principle bank exam questions, and fundamental counting principle ssc cgl.

📝 Worksheet 7 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate Advanced level

What you'll learn in this worksheet:
Your progress through Fundamental Counting Principle
Worksheet 7 of 10 (66% complete)

Question 1

A student has 6 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: 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 2

A restaurant offers 6 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: 6 options
- Second choice: 7 options
- Third choice: 2 options

Calculation:
Total ways = 6 × 7 × 2 = 84

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 7 second choices (6×7=42), and each of these can be combined with any of the 2 third choices.

Question 3

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

Calculation:
Total ways = 6 × 6 × 3 = 108

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 3 third choices.

Question 4

A car model has 5 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: 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 5

A car model has 5 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: 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 6

A student has 6 shirts, 7 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: 6 options
- Second choice: 7 options
- Third choice: 5 options

Calculation:
Total ways = 6 × 7 × 5 = 210

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 7 second choices (6×7=42), and each of these can be combined with any of the 5 third choices.

Question 7

A student has 3 shirts, 5 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: 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 8

A car model has 4 colors, 5 engine types, and 2 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: 2 options

Calculation:
Total ways = 4 × 5 × 2 = 40

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 2 third choices.

Question 9

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

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

Question 10

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 11

A student has 6 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: 6 options
- Second choice: 7 options
- Third choice: 4 options

Calculation:
Total ways = 6 × 7 × 4 = 168

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 7 second choices (6×7=42), and each of these can be combined with any of the 4 third choices.

Question 12

A student has 4 shirts, 4 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: 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 13

A student has 6 shirts, 4 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: 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 14

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

Calculation:
Total ways = 4 × 4 × 3 = 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 4 second choices (4×4=16), and each of these can be combined with any of the 3 third choices.

Question 15

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 16

A car model has 3 colors, 7 engine types, and 2 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: 7 options
- Third choice: 2 options

Calculation:
Total ways = 3 × 7 × 2 = 42

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 2 third choices.

Question 17

A car model has 5 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: 5 options
- Second choice: 5 options
- Third choice: 5 options

Calculation:
Total ways = 5 × 5 × 5 = 125

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 5 second choices (5×5=25), and each of these can be combined with any of the 5 third choices.

Question 18

A student has 3 shirts, 5 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: 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 19

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

Calculation:
Total ways = 5 × 5 × 4 = 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 5 second choices (5×5=25), and each of these can be combined with any of the 4 third choices.

Question 20

A student has 3 shirts, 7 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: 7 options
- Third choice: 5 options

Calculation:
Total ways = 3 × 7 × 5 = 105

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 5 third choices.
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