🎲 Counting & Combinatorics
Count possibilities without listing them all
🔢 The multiplication principle
If you have 3 shirts and 4 trousers, you have 3 × 4 = 12 outfits. When choices are independent, multiply.
When choosing from the same pool, be careful about order and repeats. Are we choosing different items, or can we use the same one twice?
Multiply choices together
Each independent decision creates that many times more combinations.
📝 Systematic listing
For small problems, list systematically. Use a tree diagram or organized table.
Example: Two dice can make sums from 2 to 12, but not equally likely.
- Only 1 way to get 2: (1+1)
- 6 ways to get 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
This shows why some sums are more common when you roll two dice!
⚡ Avoiding overcounting
A handshake involves 2 people. If 5 people each shake 4 hands = 20, but that counts each handshake twice (once for each person). Divide by 2 to get 10 handshakes.
Formula: n people shaking hands with each other = n(n−1)/2
Be careful: are you counting each pair once or twice?
🧠 Practice Quiz
Score: 0 / ?