Question 14
A deck consists of $3n$ cards, $n$ each colored red, green and blue in denominations $1$ through $n$. We choose a subset $S$ of the denominations and deal all cards of the chosen denominations into three equal size hands to players designated red, green and blue in such a way that no player receives a card of her own color. Prove that the number of deals for which the denominations appearing in the red player's hand are $1, 2, \dots, k$ equals $\binom{n}{k}\binom{2k}{k}$. (So it doesn't depend on the size of $S$.)