AMC10 2004 A

AMC10 2004 A · Q12

AMC10 2004 A · Q12. It mainly tests Basic counting (rules of product/sum).

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?

Henry的汉堡天堂提供汉堡时有以下调味品：番茄酱、芥末、美乃滋、西红柿、生菜、泡菜、奶酪和洋葱。顾客可以选择一个、两个或三个肉饼，以及任意组合的调味品。有多少种不同的汉堡可以点？

(A) 24 24

(B) 256 256

(D) 40320 40320

(E) 120960 120960

Answer

Correct choice: (C)

正确答案：（C）

Solution

A customer makes one of two choices for each condiment, to include it or not to include it. The choices are made independently, so there are $2^8 = 256$ possible combinations of condiments. For each of those combinations there are three choices regarding the number of meat patties, so there are altogether $(3)(256) = 768$ different kinds of hamburger.

顾客对每个调味品有两个选择，包括或不包括。选择是独立的，因此有$2^8=256$种可能的调味品组合。对于每种组合，有三种肉饼数量选择，因此总共有$(3)(256)=768$种不同的汉堡。

Topics

CP.001 Basic counting (rules of product/sum)