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

A. 105

B. 114

C. 190

D. 210

E. 380

1. 2019 AMC 8 官方解析

Alice有24颗苹果. 当她把这些苹果分给 Becky 和 Chris，使得每人手里至少有两颗，总共有多少种分法？
All three people has at least two apples, we may equivalently first assign 3 apples, one to each. Then it becomes a new problem, assigning 21 apples to 3people, each with positive numbers.
$\binom{21 - 1}{3 - 1} = \binom{20}{2} = 190$ .