AMC8 2001

AMC8 2001 · Q14

AMC8 2001 · Q14. It mainly tests Basic counting (rules of product/sum), Combinations.

Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose? Meat: beef, chicken, pork Vegetables: baked beans, corn, potatoes, tomatoes Dessert: brownies, chocolate cake, chocolate pudding, ice cream

Tyler 在自助餐队伍中选择一种肉类、两种不同的蔬菜和一种甜点。如果食物项目的顺序不重要，他可以选择多少种不同的餐点？肉类：牛肉、鸡肉、猪肉蔬菜：烤豆子、玉米、土豆、西红柿甜点：布朗尼、巧克力蛋糕、巧克力布丁、冰激凌

(A) 4 4

(B) 24 24

(D) 80 80

(E) 144 144

Answer

Correct choice: (C)

正确答案：（C）

Solution

(C) There are 3 choices for the meat and 4 for dessert. There are 6 ways to choose the two vegetables. The first vegetable may be chosen in 4 ways and the second in 3 ways. This would seem to make 12 ways, but since the order is not important the 12 must be divided by 2. Otherwise, for example, both tomatoes/corn and corn/tomatoes would be included. The 6 choices are beans/corn, beans/potatoes, beans/tomatoes, corn/potatoes, corn/tomatoes and potatoes/tomatoes. The answer is $3(4)(6)=72$.

（C）肉类有 3 种选择，甜点有 4 种选择。选择两种蔬菜有 6 种方法。第一种蔬菜有 4 种选法，第二种有 3 种选法。看起来共有 12 种，但由于顺序不重要，12 必须除以 2。否则，例如，tomatoes/corn 和 corn/tomatoes 都会被算作不同情况。6 种选择是 beans/corn、beans/potatoes、beans/tomatoes、corn/potatoes、corn/tomatoes 和 potatoes/tomatoes。答案是 $3(4)(6)=72$。

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