Problem:
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?
Answer Choices:
A.
B.
C.
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E.
Solution:
Let us assign everybody apples. This leaves us with apples. Then, we want to solve the equation , where is the number of apples that Alice gets, and so on. 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, which is given by the formula .
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions