2019 AMC 8 Problems/Problem 25

Problem 25

Alice has $24$ apples. In how many ways can she share them with Becky and Chris so that each of the people has at least $2$ apples?

Solution 1

Using Stars and bars, and removing $6$ apples so each person can have $2$ , we get the total number of ways, which is ${20 \choose 2}$ , which is equal to $\boxed{\textbf{(C) }190}$ . ~~SmileKat32

Solution 2

Let's say you assume that Alice has 2 apples. There are 19 ways to split the rest of the apples with Becky and Chris. If Alice has 3 apples, there are 18 ways to split the rest of the apples with Becky and Chris. If Alice has 4 apples, there are 17 ways to split the rest. So the total number of ways to split 24 apples between the three friends is equal to 19+18+17...……+1=20(19/2)= $\boxed{\textbf{(C)}\ 190}$

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2019 AMC 8 Problems/Problem 25

Problem 25

Solution 1

Solution 2