Nine different story books are to be shared equally among three named children, Aarav, Bela and Chirag, so that each child gets 3 books. In how many ways can this be done?

Hand out the books in turn: Aarav's 3 in $C(9,3)=84$ ways, Bela's 3 from the remaining 6 in $C(6,3)=20$ ways, and Chirag takes the last 3 in 1 way. Total = $84\times 20=1680$, which is the familiar 9!/(3! × 3! × 3!). Trap 280 = 1680/3! is the count for three UNLABELLED bundles; here the children are named, so the bundles are distinguishable and must not be divided by 3!. Trap 84 stops after the first child. Trap 362880 = 9! puts the books in a row instead of sharing them out.