Civil Service Exam (Subprofessional) Numerical Ability — Permutation & CombinationSlides
If you commute to a Civil Service Exam (Subprofessional) review centre (or watch Super Tutor on the jeepney), these Permutation & Combination slides are designed for exactly that. Each slide holds one idea, one visual cue, and one CSC-style question pattern — ready for quick bursts of review between stops.
Exam context
Civil Service Commission (CSC) runs the Career Service Examination — Subprofessional Level on Bi-annual — March and August 2026. Its Numerical Ability section sits under a "~25% weightage" weighting, and Permutation & Combination is the 7th chapter in the 9-chapter Civil Service Exam (Subprofessional) Numerical Ability rotation. The Civil Service Exam (Subprofessional) passing mark is 80%, and the most recent 2026 paper drew about 17 questions from Numerical Ability.
Permutation & Combination - Slides
Permutation and Combination are fundamental concepts in mathematics that help us count arrangements and selections. These concepts are essential for solving probability problems and are frequently tested in major Philippine examinations like UPCAT, CSE, and other entrance exams. This chapter will guide you through understanding when to use permutations versus combinations, their formulas, and practical applications in real-world scenarios.
Slides
Introduction to Permutation & Combination
Permutation and Combination are mathematical techniques used to determine the number of possible arrangements or selections from a set of objects. The key difference lies in whether the order of selection matters or not.
Notes
This introductory slide sets the foundation for understanding the difference between permutation and combination.
Topic
Introduction
Slide Id
S1
Visual Type
mermaid
Image Prompt
Slide Number
1
Mermaid Diagram
Code
mindmap root((Counting Principles)) Permutation Order Matters Arrangements Line Formation Password Creation Combination Order Does Not Matter Selection Team Formation Menu Choices Applications Probability Entrance Exams Real World Problems
Type
mermaid_mindmap
Description
Mind map showing the overview of counting principles, distinguishing between permutation and combination with their key characteristics and applications
Understanding Factorial
Factorial is a fundamental concept used in both permutation and combination calculations. It represents the number of ways to arrange n distinct objects.
Notes
Understanding factorial is crucial as it forms the basis of all permutation and combination formulas.
Topic
Factorial
Slide Id
S2
Visual Type
mermaid
Image Prompt
Slide Number
2
Mermaid Diagram
Code
flowchart TD A[n!] --> B{n = 0?} B -->|Yes| C[n! = 1] B -->|No| D[n! = n × n-1 × n-2 × ... × 1] D --> E[Example: 4! = 4 × 3 × 2 × 1 = 24] C --> F[Used in Formulas] E --> F
Type
mermaid_flowchart
Description
Flowchart showing the definition and calculation process of factorial, including the special case of 0!
What is Permutation?
In permutation, we arrange r objects from n available objects, and different orders create different arrangements. For example, ABC and BAC are different permutations.
Notes
Emphasize that in permutation, ABC and BAC are considered different arrangements.
Topic
Permutation Definition
Slide Id
S3
Visual Type
mermaid
Image Prompt
Slide Number
3
Mermaid Diagram
Code
flowchart TD A[Permutation nPr] --> B[Order Matters] B --> C[Formula: n!/(n-r)!] C --> D[Example: 5P3] D --> E[5!/(5-3)! = 5!/2!] E --> F[= 120/2 = 60] F --> G[60 different arrangements]
Type
mermaid_flowchart
Description
Flowchart illustrating the concept of permutation, its formula, and a step-by-step calculation example
Permutation Formula and Calculation
The permutation formula calculates how many ways we can arrange r objects selected from n total objects. Each step in the calculation has a specific purpose.
Notes
Practice with different values of n and r to build computational fluency.
Topic
Permutation Formula
Slide Id
S4
Visual Type
mermaid
Image Prompt
Slide Number
4
Mermaid Diagram
Code
flowchart TD A[Given: n objects, select r] --> B[Use Formula: nPr = n!/(n-r)!] B --> C[Calculate n!] C --> D[Calculate (n-r)!] D --> E[Divide: n!/(n-r)!] E --> F[Simplify to get answer] F --> G[fa:fa-check Final Result]
Type
mermaid_flowchart
Description
Step-by-step flowchart showing the calculation process for permutation problems
Permutation Example: Art Class Selection
When arranging artists for an exhibition, the position matters (first artist gets prime spot, second gets next best, etc.). This makes it a permutation problem.
Notes
Emphasize why this is permutation - the position in the exhibition matters.
Topic
Permutation Example
Slide Id
S5
Visual Type
mermaid
Image Prompt
Slide Number
5
Mermaid Diagram
Code
flowchart TD A[10 talented artists] --> B[Select 3 for exhibition] B --> C{Does order matter?} C -->|Yes - position matters| D[Use Permutation] D --> E[10P3 = 10!/(10-3)!] E --> F[= 10 × 9 × 8] F --> G[= 720 arrangements]
Type
mermaid_flowchart
Description
Problem-solving flowchart for the art class selection example, showing decision process and calculation
What is Combination?
In combination, we select r objects from n available objects, but different orders of the same selection are considered identical. For example, selecting {A,B,C} is the same as selecting {B,A,C}.
Notes
Emphasize that in combination, {A,B,C} and {B,A,C} are considered the same selection.
Topic
Combination Definition
Slide Id
S6
Visual Type
mermaid
Image Prompt
Slide Number
6
Mermaid Diagram
Code
flowchart TD A[Combination nCr] --> B[Order Does NOT Matter] B --> C[Formula: n!/r!(n-r)!] C --> D[Example: 5C3] D --> E[5!/(3! × 2!)] E --> F[= 120/(6 × 2) = 10] F --> G[10 different selections]
Type
mermaid_flowchart
Description
Flowchart illustrating the concept of combination, its formula, and a step-by-step calculation example
Combination Formula and Calculation
The combination formula divides permutation by r! to remove the effect of different arrangements of the same selection. This gives us pure selection count without considering order.
Notes
Show how combination formula relates to permutation formula divided by r!
Topic
Combination Formula
Slide Id
S7
Visual Type
mermaid
Image Prompt
Slide Number
7
Mermaid Diagram
Code
flowchart TD A[Given: n objects, select r] --> B[Use Formula: nCr = n!/r!(n-r)!] B --> C[Calculate n!] C --> D[Calculate r!] D --> E[Calculate (n-r)!] E --> F[Divide: n!/r!(n-r)!] F --> G[fa:fa-check Final Result]
Type
mermaid_flowchart
Description
Step-by-step flowchart showing the calculation process for combination problems
Combination Example: Senator Selection
When selecting senators, the order doesn't matter since all selected candidates will have the same position. What matters is who gets selected, not the order of selection.
Notes
Emphasize why this is combination - all senators have equal status regardless of selection order.
Topic
Combination Example
Slide Id
S8
Visual Type
mermaid
Image Prompt
Slide Number
8
Mermaid Diagram
Code
flowchart TD A[15 senator candidates] --> B[Select 12 for office] B --> C{Does order matter?} C -->|No - equal positions| D[Use Combination] D --> E[15C12 = 15!/(12! × 3!)] E --> F[= 15 × 14 × 13 / 3!] F --> G[= 455 selections]
Type
mermaid_flowchart
Description
Problem-solving flowchart for the senator selection example, showing decision process and calculation
Key Differences: Permutation vs Combination
The fundamental difference is whether the order of selection matters. This determines which formula to use and affects the final answer significantly.
Notes
This is a critical slide for helping students decide which formula to use.
Topic
Permutation vs Combination
Slide Id
S9
Visual Type
mermaid
Image Prompt
Slide Number
9
Mermaid Diagram
Code
flowchart TD A[Problem Given] --> B{Does ORDER matter?} B -->|YES| C[PERMUTATION] B -->|NO| D[COMBINATION] C --> E[nPr = n!/(n-r)!] D --> F[nCr = n!/r!(n-r)!] E --> G[Higher Result] F --> H[Lower Result] G --> I[fa:fa-star Answer] H --> I
Type
mermaid_flowchart
Description
Decision tree flowchart helping students choose between permutation and combination based on whether order matters
Identifying Keywords in Problems
Recognizing key words and phrases in problems helps determine whether to use permutation or combination. Understanding the context is equally important.
Notes
Students should practice identifying these keywords in various problem contexts.
Topic
Problem Identification
Slide Id
S10
Visual Type
mermaid
Image Prompt
Slide Number
10
Mermaid Diagram
Code
mindmap root((Problem Keywords)) Permutation Words Arrange Position Rank Order Line up Sequence Combination Words Select Choose Pick Team Committee Group Context Clues Different roles Equal status Hierarchy Random selection
Type
mermaid_mindmap
Description
Mind map showing keywords and context clues that help identify whether a problem requires permutation or combination
Consecutive Numbers in Permutation & Combination
Understanding consecutive numbers is important when solving problems involving sequences. These concepts often appear in combination with permutation and combination problems.
Notes
Consecutive numbers often appear in more complex permutation and combination problems.
Topic
Consecutive Numbers
Slide Id
S11
Visual Type
mermaid
Image Prompt
Slide Number
11
Mermaid Diagram
Code
flowchart TD A[Consecutive Numbers] --> B[Regular: n, n+1, n+2] A --> C[Even: n, n+2, n+4] A --> D[Odd: n, n+2, n+4] B --> E[Example: 3,4,5,6] C --> F[Example: 8,10,12,14] D --> G[Example: 7,9,11,13] E --> H[Use in P&C problems] F --> H G --> H
Type
mermaid_flowchart
Description
Flowchart showing different types of consecutive numbers and how they're formed
Probability Connection
Permutation and combination provide the tools to count total possible outcomes and favorable outcomes in probability problems. This connection is crucial for solving complex probability questions.
Notes
This connection to probability shows the practical importance of mastering P&C concepts.
Topic
Probability Connection
Slide Id
S12
Visual Type
mermaid
Image Prompt
Slide Number
12
Mermaid Diagram
Code
flowchart TD A[Probability Problem] --> B[Count Total Outcomes] A --> C[Count Favorable Outcomes] B --> D{Order matters?} C --> D D -->|Yes| E[Use Permutation] D -->|No| F[Use Combination] E --> G[Calculate P = F/T] F --> G G --> H[fa:fa-check Final Probability]
Type
mermaid_flowchart
Description
Flowchart showing how permutation and combination are used in probability calculations
Common Mistakes to Avoid
Students often make these common errors when solving permutation and combination problems. Being aware of these pitfalls helps avoid mistakes during exams.
Notes
Review these mistakes regularly to build good problem-solving habits.
Topic
Common Mistakes
Slide Id
S13
Visual Type
mermaid
Image Prompt
Slide Number
13
Mermaid Diagram
Code
flowchart TD A[Common Mistakes] --> B[fa:fa-times Wrong Formula Choice] A --> C[fa:fa-times Factorial Errors] A --> D[fa:fa-times Calculation Mistakes] B --> E[Read problem carefully] C --> F[Remember 0! = 1] D --> G[Double-check arithmetic] E --> H[fa:fa-check Correct Solution] F --> H G --> H
Type
mermaid_flowchart
Description
Flowchart highlighting common mistakes and how to avoid them in permutation and combination problems
Exam Tips and Strategies
Success in permutation and combination problems requires strategic thinking and efficient calculation techniques. These tips help maximize performance during exams.
Notes
These strategies are particularly useful for timed exams like UPCAT and other entrance tests.
Topic
Exam Strategies
Slide Id
S14
Visual Type
mermaid
Image Prompt
Slide Number
14
Mermaid Diagram
Code
flowchart TD A[fa:fa-book Exam Problem] --> B[Read Carefully] B --> C[Identify Keywords] C --> D{Order Matters?} D -->|Yes| E[fa:fa-calculator Permutation nPr] D -->|No| F[fa:fa-calculator Combination nCr] E --> G[Simplify Before Calculate] F --> G G --> H[fa:fa-check Verify Answer] H --> I[fa:fa-star Final Answer]
Type
mermaid_flowchart
Description
Strategic approach flowchart for solving permutation and combination problems in exams
Real-World Applications
Permutation and combination concepts appear frequently in real-world scenarios. Understanding these applications helps students see the practical value of these mathematical tools.
Notes
Connecting math to real-world applications increases student engagement and understanding.
Topic
Real-World Applications
Slide Id
S15
Visual Type
mermaid
Image Prompt
Slide Number
15
Mermaid Diagram
Code
mindmap root((Real World Uses)) Security Passwords PIN codes Lock combinations Education Class arrangements Team formation Committee selection Business Product bundling Menu combinations Staff scheduling Entertainment Game tournaments Seating charts Event planning
Type
mermaid_mindmap
Description
Mind map showing various real-world applications of permutation and combination concepts across different fields
Chapter Summary and Key Takeaways
This chapter covered the fundamental concepts of permutation and combination, their formulas, and applications. These tools are essential for counting problems and form the basis for more advanced mathematical concepts.
Notes
This summary slide reinforces the main concepts and prepares students for further study.
Topic
Summary
Slide Id
S16
Visual Type
none
Image Prompt
Slide Number
16
Mermaid Diagram
Type
none
References
- Civil Service Institute Civil Service Complete Exam Reviewer - Combination Section
- NCV Civil Service Worded Problems - Probability Section
- Philippine entrance exam syllabi (UPCAT, CSE, LET, NLE, NMAT, ACET, USTET)
- Standard Grade 12 Mathematics curriculum Philippines
In summary
Mastering permutation and combination is crucial for success in mathematics and entrance examinations. These concepts provide the foundation for counting problems, probability calculations, and many real-world applications. The key to success is understanding when order matters (permutation) versus when it doesn't (combination), and practicing with various problem types. Regular practice with the formulas nPr = n!/(n-r)! and nCr = n!/[r!(n-r)!] will build confidence and speed in solving these problems. Remember to read problems carefully, identify keywords, and always verify your answers make sense in the context of the problem.
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Word Problems — Speed/Distance/Age, Discount & Interest
Next chapter
Geometry — Perimeter, Area, Circumference & Volume
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