2004 AMC 10A 第 12 题

Question

Henry’s Hamburger Heaven 提供以下汉堡配料：番茄酱、芥末酱、蛋黄酱、番茄、生菜、腌黄瓜、奶酪和洋葱。顾客可以选择一块、两块或三块肉饼，并可选择任意一组配料。共有多少种不同的汉堡可以点？

Henry’s Hamburger Heaven offers its hamburgers with the following condiments: ketchup, mustard, mayonnaise, tomato, lettuce, pickles, cheese, and onions. A customer can choose one, two, or three meat patties, and any collection of condiments. How many different kinds of hamburgers can be ordered?

24

256

768

40{,}320

120{,}960

答案：C

知识点：乘法原理子集

难度评级：1190

小提示：

8

种配料中每一种都可以选择或不选择。

Each of the

8

condiments is independently included or left out

大提示：

将

2^8

种配料选择乘以

3

种肉饼数量选择。

Multiply the

2^8

condiment choices by the

3

choices of patty count

解答：

8

种配料各自独立选择是否加入，共有

2^8 = 256

种配料组合。

每种组合还有

3

种肉饼数量选择，所以汉堡种类为

3 \times 256 = 768\text{。}

所以正确答案是 C。

Each of the

8

condiments is independently in or out, giving

2^8 = 256

condiment combinations.

For each of these there are

3

choices of patty count, so the number of hamburgers is

3 \times 256 = 768.

Thus, the correct answer is C.

2004 AMC 10A 第 12 题

答案：C

难度评级：1190

小提示：

大提示：

解答：

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