BFP Entrance Exam Numerical Ability — Permutation & CombinationCheat Sheet
A printable cheat sheet for Permutation & Combination, built for BFP Entrance Exam reviewers who want one go-to reference in the final stretch. Covers formulas, key definitions, common question types, and the Bureau of Fire Protection (BFP)-specific twists you will see on BFP Entrance Exam day.
Exam context
The Bureau of Fire Protection Entrance Examination is conducted by Bureau of Fire Protection (BFP) and is scheduled for Announced by BFP per cycle. The Numerical Ability subtest is marked as "Core" in the official pattern, and Permutation & Combination appears in position 7th of 9 in the BFP Entrance Exam Numerical Ability review rotation. Passing mark: BFP-set percentile (typically 70%+). Recent BFP Entrance Exam 2026 papers have drawn roughly a meaningful share of questions from this subject.
Permutation & Combination - Cheat sheet
Your last-minute revision companion for mastering Permutation & Combination problems in Civil Service and college entrance exams.
Sections
Formulas
Formula
n! = n × (n-1) × (n-2) × ... × 2 × 1
Meaning
n! = factorial of n, multiply all positive integers from n down to 1
Watch Out
Remember 0! = 1, not 0
When To Use
Foundation for all permutation and combination calculations
Common Values
Value
1
Symbol
0!
Quantity
0 factorial
Value
1
Symbol
1!
Quantity
1 factorial
Value
120
Symbol
5!
Quantity
5 factorial
Section Title
Factorials
Important Facts
- 0! = 1 by definition
- 1! = 1
- Factorials grow extremely rapidly
- Used in both permutations and combinations
Key Definitions
Term
Factorial
Example
5! = 5 × 4 × 3 × 2 × 1 = 120
Definition
Product of all positive integers less than or equal to a given number
Formulas
Formula
nPr = n!/(n-r)!
Meaning
n = total objects, r = objects selected, order matters
Watch Out
Don't confuse with combinations - permutations care about order
When To Use
When arrangement order is important (president, VP, secretary)
Section Title
Permutations
Important Facts
- Order is important in permutations
- More permutations than combinations for same n and r
- Used for arrangements, rankings, positions
- Keywords: arrange, order, sequence, first/second/third
Key Definitions
Term
Permutation
Example
ABC and BAC are different arrangements
Definition
Arrangement of objects where order matters
Formulas
Formula
nCr = n!/[r!(n-r)!]
Meaning
n = total objects, r = objects selected, order doesn't matter
Watch Out
Remember the extra r! in denominator compared to permutations
When To Use
When selecting groups where order is not important
Section Title
Combinations
Important Facts
- Order is not important in combinations
- Always fewer combinations than permutations
- Used for selections, groups, teams
- Keywords: select, choose, pick, combination, group
Key Definitions
Term
Combination
Example
Selecting 3 people from 10 for a committee
Definition
Selection of objects where order doesn't matter
Section Title
Problem-Solving Strategies
Important Facts
- If order matters, use permutation
- If order doesn't matter, use combination
- Read problem carefully for context clues
- Practice identifying keywords
- Set up the formula correctly before calculating
Key Definitions
Term
Permutation Keywords
Example
How many ways to arrange 5 books on a shelf?
Definition
Arrange, order, sequence, rank, position, first/second/third
Term
Combination Keywords
Example
How many ways to select 3 students from 10?
Definition
Select, choose, pick, group, team, committee
Must Remember
- 0! = 1 (special case, memorize this)
- Permutation formula: nPr = n!/(n-r)!
- Combination formula: nCr = n!/[r!(n-r)!]
- Order matters = Permutation, Order doesn't matter = Combination
- Permutation keywords: arrange, order, rank, position
- Combination keywords: select, choose, pick, group
- Always check if r ≤ n in your problem
- Combinations have extra r! in denominator vs permutations
- Read problem context carefully to identify which to use
- Practice canceling factorials to simplify calculations
Last Minute Tips
- Circle keywords in the problem - they tell you permutation vs combination
- For large numbers, cancel common factors in factorials before multiplying
- Double-check your formula setup before calculating
- If stuck, ask 'Does order matter?' - this determines your approach
- Practice common values like 5!, 6!, 7! for quick mental calculation
Comparison Tables
Rows
Values
- Matters
- Doesn't matter
Property
Order
Values
- nPr = n!/(n-r)!
- nCr = n!/[r!(n-r)!]
Property
Formula
Values
- Arrange, order, rank
- Select, choose, pick
Property
Keywords
Values
- More arrangements
- Fewer selections
Property
Result
Values
- President, VP, Secretary
- Committee members
Property
Example
Columns
- Aspect
- Permutation
- Combination
Table Title
Permutation vs Combination
Previous chapter
Word Problems — Speed/Distance/Age, Discount & Interest
Next chapter
Geometry — Perimeter, Area, Circumference & Volume
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