Combinatorics & Probability
📋 What it is
PERMUTATIONS count arrangements (order matters); COMBINATIONS count selections (order does not).
🗣️ Coach says
Combinatorics is advanced counting. If order matters — a race podium — you count PERMUTATIONS. If it does not — a pizza’s toppings — you count COMBINATIONS, which are always fewer. Probability then divides "outcomes you want" by "total outcomes". Getting the count right is the hard part; the division is easy.
🧠 Memory hook
Order matters → permutation. Order ignored → combination (fewer). Probability = wanted ÷ total.
😂 Giggle
Why was the counting problem so tired?
It had too many possibilities to consider!
😲 Whoa!
There are more ways to shuffle a 52-card deck than there are atoms on Earth — about 8 followed by 67 zeros.
✅ Quick check: Choosing 2 friends from 3 for a team (order does not matter) — how many ways?
Say your answer out loud first — then reveal.
3 ways: {A,B}, {A,C}, {B,C}.
This is a combination — order is ignored, so {A,B} and {B,A} count once.
🪄 Trick question: Do the arrangements "AB" and "BA" count as the same COMBINATION?
Careful — think it through, then reveal.
Yes — combinations ignore order, so AB and BA are one combination.
Only permutations treat AB and BA as different.
🧪 Try it! (2 minutes)
List every 2-topping combo you can make from 4 toppings. You should find 6.