2019 AMC 8 Problems/Problem 25
Problem 25
Alice has apples. In how many ways can she share them with Becky and Chris so that each of the people has at least apples?
Solution 1
Using Stars and bars, and removing apples so each person can have , we get the total number of ways, which is , which is equal to . ~~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)=~heeeeeeheeeeeee