2019 AMC 8 第 25 题
先试着解答 2019 AMC 8 第 25 题，然后核对你的答案与视频与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2019 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
25.
Alice 有 个苹果。她可以用多少种方式把这些苹果分给 Becky、Chris 和自己，使得三个人每人至少有两个苹果？
Alice has apples. In how many ways can she share them with Becky and Chris so that each of the three people has at least two apples?
答案：C
小提示：
先给每个人 个苹果
Give each person apples first
大提示：
用两个隔板分配剩下的苹果
Distribute the remaining apples with two dividers
视频讲解：
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文字解答：
先给三个人每人 个苹果，剩下 个。
接下来我们要解方程 其中 、 和 分别是 Alice、Becky 和 Chris 额外得到的苹果数。
因为每人至少两个苹果的条件已经满足，所以这些变量都是非负整数。
由隔板法，方案数为
正确答案是 C。
Let us assign everybody apples. This leaves us with apples.
Then, we want to solve where and are the additional apples given to Alice, Becky, and Chris.
Note that these are all nonnegative, since we already satisfied the only condition we needed to.
We can use stars and bars to get the number of solutions as
Thus, the correct answer is C.
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