Civil Service Exam (Subprofessional) Numerical Ability — Permutation & CombinationMemory Anchors

Tags

• definition
• concept

Topic

Basic Concepts

Concept

Permutation vs Combination - Order Matters

Anchor Id

A1

Difficulty

easy

Memory Aid

PROM - Permutation is about Position, Ranking, Order Matters. CHOOSE - Combination is about Choosing, no Order, Only Selection Matters

Anchor Type

acronym

Why It Works

The acronyms PROM and CHOOSE help distinguish the key difference - permutations care about order (like a prom lineup), combinations just care about selection (like choosing friends)

Example Usage

If the problem asks 'In how many ways can 5 students be arranged in a line?' - think PROM (order matters), use permutation

Recall Trigger

When you see arrangement/ranking words, think PROM. When you see selection/choosing words, think CHOOSE

Tags

• formula
• visualization

Topic

Permutation Formula

Concept

Permutation Formula nPr = n!/(n-r)!

Anchor Id

A2

Difficulty

medium

Memory Aid

Picture a PARKING lot with n spaces. You want to park r cars in specific spots. First car has n choices, second has (n-1), third has (n-2), etc. Stop after r cars, so divide by what's left (n-r)!

Anchor Type

visual_association

Why It Works

Visual imagery of parking cars in specific spots reinforces that order matters and helps remember why we divide by (n-r)!

Example Usage

For '5 students in 3 chairs': Picture parking 3 cars in a 5-space lot - first car has 5 spots, second has 4, third has 3. Answer: 5×4×3 = 60

Recall Trigger

Think of a parking lot when you see permutation problems

Tags

• formula
• story

Topic

Combination Formula

Concept

Combination Formula nCr = n!/(r!(n-r)!)

Anchor Id

A3

Difficulty

medium

Memory Aid

Coach Ramirez needs to CHOOSE r players from n team members for a group photo. He has n! ways to arrange everyone, but divides by r! (arrangements within chosen group don't matter) and (n-r)! (arrangements of those not chosen don't matter)

Anchor Type

micro_story

Why It Works

The story explains why we divide by both r! and (n-r)! - because internal arrangements don't matter in combinations

Example Usage

For 'choose 3 senators from 15 candidates': Coach has 15! ways to arrange all, divide by 3! (chosen group arrangements) and 12! (non-chosen arrangements)

Recall Trigger

Think of Coach Ramirez choosing players when you need the combination formula

Tags

• formula
• rhyme

Topic

Factorial

Concept

Factorial n! = n × (n-1) × (n-2) × ... × 1

Anchor Id

A4

Difficulty

easy

Memory Aid

Factorial's fun, it's easy to see, multiply down from n to 1, 2, 3! Start with n, go down one by one, stop at 1 and you are done!

Anchor Type

rhyme

Why It Works

Rhymes create rhythm and melody that make information stick in memory longer

Example Usage

For 5!: 'Start with 5, go down one by one' = 5×4×3×2×1 = 120

Recall Trigger

Sing the factorial song when computing n!

Tags

• keywords
• identification

Topic

Problem Identification

Concept

Keywords for Permutation Problems

Anchor Id

A5

Difficulty

easy

Memory Aid

ARAB - Arrange, Rank, Align, By position. These words signal permutation because they involve ORDER

Anchor Type

mnemonic

Why It Works

Grouping similar keywords helps quick identification of problem type during time-pressured exams

Example Usage

Problem says 'arrange 7 books on a shelf' - ARAB word 'arrange' signals permutation

Recall Trigger

When you see ARAB words, use permutation formulas

Tags

• keywords
• identification

Topic

Problem Identification

Concept

Keywords for Combination Problems

Anchor Id

A6

Difficulty

easy

Memory Aid

SPICE - Select, Pick, Involve, Choose, Elect. These words signal combination because order doesn't matter

Anchor Type

mnemonic

Why It Works

SPICE is memorable and groups the most common combination keywords together

Example Usage

Problem says 'select 5 committee members' - SPICE word 'select' signals combination

Recall Trigger

When you see SPICE words, use combination formulas

Tags

• special_case
• analogy

Topic

Special Cases

Concept

When n = r in Permutations

Anchor Id

A7

Difficulty

medium

Memory Aid

Like arranging all your family members for a photo - if you have 5 family members and 5 positions, it's just 5! ways to arrange everyone

Anchor Type

analogy

Why It Works

Family photo is relatable and shows why nPn = n! (everyone gets arranged)

Example Usage

Arrange 6 people in 6 chairs: 6P6 = 6! = 720

Recall Trigger

Think family photo when n = r

Tags

• pattern
• visualization

Topic

Consecutive Numbers

Concept

Consecutive Numbers Properties

Anchor Id

A8

Difficulty

medium

Memory Aid

Picture a ladder - each rung is exactly 1 step apart. Consecutive even numbers are like a ladder with rungs 2 steps apart (2,4,6,8). Consecutive odd numbers are also 2 steps apart (1,3,5,7)

Anchor Type

visual_association

Why It Works

Visual ladder reinforces the consistent spacing between consecutive numbers

Example Usage

Three consecutive numbers sum to 18: Let middle rung be n, then (n-1) + n + (n+1) = 18

Recall Trigger

Think of climbing a ladder when dealing with consecutive numbers

Tags

• formula
• analogy

Topic

Probability

Concept

Probability Formula P(E) = Favorable/Total

Anchor Id

A9

Difficulty

easy

Memory Aid

Probability is like your chances of getting your favorite ulam in the cafeteria - it's the number of dishes you like divided by all available dishes

Anchor Type

analogy

Why It Works

Uses familiar Filipino school experience to make abstract probability concrete

Example Usage

Probability of rolling even number on dice: 3 favorable (2,4,6) ÷ 6 total = 1/2

Recall Trigger

Think cafeteria choices when calculating probability

Tags

• shortcut
• calculation

Topic

Calculation Shortcuts

Concept

Combination Problems with Large Numbers

Anchor Id

A10

Difficulty

medium

Memory Aid

For nCr calculations, CANCEL before calculating: nCr = nC(n-r). Choose the smaller r. Example: 10C7 = 10C3 (much easier to calculate)

Anchor Type

chunking

Why It Works

Chunking breaks complex calculations into smaller, manageable pieces

Example Usage

15C12 = 15C3 = (15×14×13)/(3×2×1) = 455 (much easier than calculating 15C12 directly)

Recall Trigger

Always choose the smaller number when calculating nCr

Tags

• special_case
• story

Topic

Special Cases

Concept

Zero Factorial 0! = 1

Anchor Id

A11

Difficulty

hard

Memory Aid

Maria organized a party but 0 friends showed up. How many ways can she arrange 0 people? There's exactly 1 way - the empty arrangement! That's why 0! = 1

Anchor Type

micro_story

Why It Works

Story makes the counterintuitive fact that 0! = 1 memorable and logical

Example Usage

When calculating 5C5 = 5!/(5!×0!) = 120/(120×1) = 1

Recall Trigger

Think of Maria's empty party when you see 0!

Tags

• formula
• visualization

Topic

Probability

Concept

Multiple Events Probability P(A and B) = P(A) × P(B)

Anchor Id

A12

Difficulty

medium

Memory Aid

Picture two bridges you must cross to reach your destination. Your chance of crossing both is the probability of crossing the first bridge TIMES the probability of crossing the second bridge

Anchor Type

visual_association

Why It Works

Visual metaphor of crossing bridges reinforces multiplication rule for independent events

Example Usage

Probability of rolling two 6's: (1/6) × (1/6) = 1/36

Recall Trigger

Think crossing two bridges for multiple events

Tags

• identification
• method_of_loci

Topic

Problem Identification

Concept

Distinguishing Arrangement Problems

Anchor Id

A13

Difficulty

medium

Memory Aid

Walk through your classroom: (1) At the door - are we ENTERING people in specific POSITIONS? (Permutation). (2) At your desk - are we just SELECTING a GROUP without caring about positions? (Combination). (3) At the blackboard - does the problem mention ARRANGEMENTS or RANKINGS? (Permutation)

Anchor Type

method_of_loci

Why It Works

Method of loci uses familiar spatial memory to organize decision-making process

Example Usage

Students for debate team positions (door = positions matter = Permutation) vs students for science club (desk = group selection = Combination)

Recall Trigger

Take a mental walk through your classroom to categorize problems

Tags

• formula
• analogy

Topic

Consecutive Numbers

Concept

Sum of Consecutive Numbers Formula

Anchor Id

A14

Difficulty

medium

Memory Aid

Consecutive numbers are like rice grains in a line. If you have n grains, the middle grain represents the average. The sum is n × (average) = n × (first + last)/2

Anchor Type

analogy

Why It Works

Rice grains are familiar to Filipino students and visualizing the middle grain helps remember the averaging concept

Example Usage

Sum of consecutive numbers 5, 6, 7: 3 × (5+7)/2 = 3 × 6 = 18

Recall Trigger

Think rice grains in a line for consecutive number sums

Tags

• formula
• story

Topic

Work Problems

Concept

Work Problems Formula 1/t₁ + 1/t₂ = 1/t₃

Anchor Id

A15

Difficulty

hard

Memory Aid

Juan can paint a fence alone in 6 hours (works at rate 1/6 per hour). Maria can do it in 4 hours (rate 1/4 per hour). Together, their combined rate is 1/6 + 1/4 = 1/t, where t is time working together

Anchor Type

micro_story

Why It Works

Concrete story with Filipino names makes abstract work rate concept tangible

Example Usage

If A finishes job in 3 hours and B in 6 hours: 1/3 + 1/6 = 1/t → t = 2 hours together

Recall Trigger

Think Juan and Maria painting fence together

Tags

• circular
• visualization

Topic

Special Arrangements

Concept

Circular Arrangements (n-1)!

Anchor Id

A16

Difficulty

hard

Memory Aid

Picture friends sitting around a circular table for kamayan dinner. One person's position is fixed (like 12 o'clock), so only (n-1) people need arranging. It's like a regular line with one position locked

Anchor Type

visual_association

Why It Works

Familiar Filipino dining tradition makes circular permutation memorable, and fixing one position is intuitive

Example Usage

Arrange 5 people around circular table: Fix one person, arrange remaining 4: (5-1)! = 4! = 24 ways

Recall Trigger

Think kamayan dinner table when arranging in circles

Tags

• organization
• table

Topic

Age Problems

Concept

Age Problems Setup

Anchor Id

A17

Difficulty

medium

Memory Aid

AGE problems follow pattern: Now-Past-Future table. Make columns for each person and rows for time periods. Let x = current age of one person, express others in terms of x

Anchor Type

chunking

Why It Works

Systematic table organization breaks complex age relationships into manageable pieces

Example Usage

Ana is 3 times older than Ben. In 5 years, Ana will be twice as old. Table helps set up: Ana now = 3x, Ben now = x

Recall Trigger

Draw a Now-Past-Future table for age problems

Tags

• facts
• mnemonic

Topic

Probability

Concept

Card Problems - Standard Deck Facts

Anchor Id

A18

Difficulty

easy

Memory Aid

SHED the cards: 52 total, Hearts and Diamonds are red (26), Spades and Clubs are black (26), Each suit has 13 cards, 4 suits total, Deck has 4 of each rank

Anchor Type

mnemonic

Why It Works

SHED organizes all key facts about card decks in one memorable acronym

Example Usage

Probability of drawing a Queen: 4 Queens in 52 cards = 4/52 = 1/13

Recall Trigger

SHED cards to remember deck composition

Tags

• dice
• visualization

Topic

Probability

Concept

Dice Problems - All Outcomes

Anchor Id

A19

Difficulty

medium

Memory Aid

Picture a dice as a small bahay kubo with 6 faces. Rolling two dice is like having two bahay kubos, giving you 6 × 6 = 36 possible combinations. Each outcome is equally likely

Anchor Type

visual_association

Why It Works

Cultural reference to bahay kubo makes dice memorable, and visualization of two houses helps remember why outcomes multiply

Example Usage

Probability of rolling sum of 7 with two dice: 6 ways to get 7 out of 36 total = 6/36 = 1/6

Recall Trigger

Think two bahay kubos for two-dice problems

Tags

• repetition
• analogy

Topic

Special Arrangements

Concept

Repetition in Arrangements

Anchor Id

A20

Difficulty

hard

Memory Aid

Arranging letters with repetition is like organizing identical twins in a photo - you can't tell the twins apart, so divide by 2! for each set of twins. For n total letters with groups of identical letters, divide n! by the factorial of each group size

Anchor Type

analogy

Why It Works

Twin analogy makes clear why we divide by factorials of repeated elements

Example Usage

Arrange letters in BANANA: 6 letters total, but 3 A's and 2 N's repeat. Answer: 6!/(3!×2!) = 720/12 = 60

Recall Trigger

Think organizing identical twins when letters repeat

Formula

nPr = n!/(n-r)!

Mnemonic

Permutation: Park n cars, Remove (n-r) unused spaces

When To Use

When order matters in selection (arrangements, rankings, positions)

What Each Part Means

n = total items, r = items selected, n! = all arrangements, (n-r)! = what we don't use

Formula

nCr = n!/(r!(n-r)!)

Mnemonic

Combination: Choose from n items, Cancel arrangements in r selected and (n-r) not selected

When To Use

When order doesn't matter in selection (choosing groups, committees, teams)

What Each Part Means

n! = all arrangements, r! = arrangements within selection, (n-r)! = arrangements of non-selected

Formula

P(E) = Favorable/Total

Mnemonic

Probability: Favorable outcomes over Total outcomes

When To Use

For any probability calculation with equally likely outcomes

What Each Part Means

Favorable = outcomes we want, Total = all possible outcomes

Formula

1/t₁ + 1/t₂ = 1/t₃

Mnemonic

Work rates add up: individual Work rates combine to Total work rate

When To Use

When two or more people/machines work together on the same job

What Each Part Means

t₁, t₂ = individual completion times, t₃ = combined completion time

Chain Title

Steps to Solve Permutation Problems

Recall Test

What are the 5 steps when you see words like 'arrange' or 'rank'?

Memory Chain

A Rabbit Always Brings Carrots - Arabs Respect Amazing Brain Calculations

Items To Remember

• Identify keywords (ARAB)
• Check if order matters
• Use nPr formula
• Calculate n!/(n-r)!
• Simplify the answer

Chain Title

Steps to Solve Combination Problems

Recall Test

What are the 5 steps when you see words like 'select' or 'choose'?

Memory Chain

Smart People In Class Excel - Spice Produces Incredible Culinary Excellence

Items To Remember

• Identify keywords (SPICE)
• Confirm order doesn't matter
• Use nCr formula
• Calculate n!/(r!(n-r)!)
• Use shortcuts when possible

Chain Title

Consecutive Number Problem Steps

Recall Test

What are the 5 steps to solve consecutive number problems?

Memory Chain

Let X Express Equations Systematically Finding - Little Xavier Eagerly Solves Fun problems

Items To Remember

• Let x = first number
• Express others as x+1, x+2, etc
• Set up equation with given condition
• Solve for x
• Find all requested numbers

Chain Title

Work Problem Solution Steps

Recall Test

What are the 5 steps to solve work rate problems?

Memory Chain

Industrious Workers Add Rates Successfully Together - I Will Add Rates Swiftly Together

Items To Remember

• Identify individual work rates
• Add rates for combined work
• Set up equation 1/t₁ + 1/t₂ = 1/t₃
• Solve for unknown time
• Check answer makes sense

Chain Title

Age Problem Solution Method

Recall Test

What are the 5 systematic steps for age word problems?

Memory Chain

Never Push Forward Looking Eagerly Ahead - Nice People Find Life Experiences Amazing

Items To Remember

• Create Now-Past-Future table
• Let x = one person's current age
• Express all ages in terms of x
• Set up equation from given relationship
• Solve and verify