Counting Principles
Grades 9–11 Probability Counting
How many 2-course meals from 4 starters and 3 mains? Multiply: 4 × 3 = 12. Every starter pairs with every main — that's the multiplication principle, the root of all counting.
Order matters → permutations
Podium places from 8 runners: 8 choices for gold, then 7 for
silver, then 6 for bronze → 8 × 7 × 6 = 336 arrangements.
Written 8P3. Picking all 8 places:
8! = 40,320 — that's factorial:
8 × 7 × 6 × … × 1.
Order doesn't matter → combinations
Choosing 3 toppings from 6 — pepperoni+mushroom+olive is the same pizza regardless of pick order. Divide the permutations by the ways to arrange the picks:
4 shirts × 3 pants × 2 hats = ___ outfits
5 books arranged on a shelf: 5! = ___
Choose 2 of 6 people for a team: 6C2 = ___
Awarding gold/silver/bronze to 10 runners is a:
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