Alice has 24 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?
(A)105(B)114(C)190(D)210(E)380 A+B+C=24A≥2B≥2C≥2 A+B+C=24A≥2,B≥2,C≥2
LetA′=A−1,B′=B−1,C′=C−1
ThenA′+B′+C′=21A′≥1,B′≥1,C′≥1 (220)=220⋅19=190