Question

一位甜点师从星期日开始为一周中的每天准备甜点。每天的甜点可以是蛋糕、派、冰淇淋或布丁。连续两天不能供应同一种甜点。因为生日聚会，星期五必须供应蛋糕。这一周有多少种不同的甜点菜单？

A dessert chef prepares the dessert for every day of a week starting with Sunday. The dessert each day is either cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row. There must be cake on Friday because of a birthday. How many different dessert menus for the week are possible?

$729$

$972$

$1024$

$2187$

$2304$

答案：A

知识点：有限制的排列乘法原理逆推法

难度评级：1140

解答：

星期五固定为蛋糕。星期六不能是蛋糕，所以有 $3$ 种选择。

从星期五往前，星期四有 $3$ 种选择；再往前每一天也都只有不能等于后一日的限制，因此各有三种选择。星期日到星期四共 $5$ 天，所以总数为 $3^5\cdot 3 = 729$ 。

所以正确答案是 A。

We know that there must be cake served on Friday, and as such, on Saturday, we cannot have cake. Therefore, we have $3$ choices for Saturday's menu.

Furthermore, for each of the $5$ previous days, we could go backwards and have $3$ choices on each day, making the total number of choices $3^5\cdot 3 = 729.$

Thus, the correct answer is A .

2012 AMC 10B 第 11 题

答案：A

难度评级：1140

解答：

其他年份的第 11 题