The Principle of Counting
Master the real foundation of combinations. If this becomes automatic, permutations and combinations become almost trivial.
Master Counting Principle
This is the real foundation. If this becomes automatic, permutations and combinations become almost trivial.
Core Idea
If one thing can happen in a ways and another thing can happen in b ways, then total ways: a × b
Real Intuition
Suppose you have 3 shirts and 2 pants. How many outfits?
Your brain should SEE this:
Shirt1 → Pant1, Pant2
Shirt2 → Pant1, Pant2
Shirt3 → Pant1, Pant2
So: 3 × 2 = 6
Another Example
2 burgers
3 drinks
4 desserts
Total meals?
Your brain should think:
For EACH burger: 3 drink choices
For EACH drink: 4 dessert choices
Your New Mental Model
Practice Until Automatic
Do these mentally.
Practice 1
4 t-shirts, 5 jeans. Total outfits?
Answer: 4 × 5 = 20
Practice 2
3 starters, 2 main courses, 4 desserts. Total meals?
Answer: 3 × 2 × 4 = 24
Practice 3
A password has: 2 letters, 3 digits.
If each letter has 26 choices and each digit has 10 choices, total passwords?
Your brain should think: 26 × 26 × 10 × 10 × 10 = 26² × 10³