Problem 20 · 2010 Math Kangaroo
Stretch
Counting & Probability
careful-counting
In a pizzeria there is a basic pizza with tomato and cheese. It can be ordered with exactly one or exactly two of the following toppings: anchovies, artichokes, mushrooms or capers. The pizza comes in three sizes. How many different types of pizza are offered in total?
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Answer: A — 30
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Hint 1 of 2
Count the topping choices first: either pick one topping, or pick a pair of two toppings.
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Hint 2 of 2
Once you know how many topping choices there are, each one comes in 3 sizes.
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Approach: count topping choices, then multiply by sizes
- Picking one topping: 4 ways. Picking a pair from the 4 toppings: the pairs are \(\{1,2\},\{1,3\},\{1,4\},\{2,3\},\{2,4\},\{3,4\}\), so 6 ways.
- That is \(4 + 6 = 10\) topping choices.
- Each choice comes in 3 sizes, so \(10 \times 3 = 30\) pizzas — the answer is A.
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