Counting and Patterns
📋 What it is
The MULTIPLICATION PRINCIPLE: if one choice has m options and the next has n, together they have m × n outcomes.
🗣️ Coach says
Discrete math teaches you to count WITHOUT listing. If you have 3 shirts and 4 pants, you have 3 × 4 = 12 outfits — you never write them all out. This "multiply the choices" idea powers permutations, passwords, and probability. Spotting the pattern is faster and less error-prone than counting one by one.
🧠 Memory hook
Count by MULTIPLYING choices, not by listing. 3 shirts × 4 pants = 12 outfits.
😂 Giggle
What did the Venn diagram say at the party?
"Let's find what we have in common!"
😲 Whoa!
A 4-digit PIN has 10 × 10 × 10 × 10 = 10,000 possibilities — which is exactly why banks add a "3 tries" lock.
✅ Quick check: A menu has 3 mains and 5 drinks. How many main-and-drink combos are there?
Say your answer out loud first — then reveal.
15 (3 × 5).
The multiplication principle: multiply the options at each independent choice.
🧪 Try it! (2 minutes)
Count your possible outfits from your real shirts × pants by multiplying — then check by picturing a few.