How do you calculate the odds of this happening in poker?
There are 4 players. Each of them had a pair each of the cards K,Q,A,10 in pre flop itself. The cards on the table are 5, 10, A, Q J So the winner had a straight. But the other three players each had a three of a kind. what are the odds of this happening, and how can we calculate that?
Hands of players: $$ 1:\fbox{$\color{red} {\substack{K\\\heartsuit}}$},\fbox{$\substack{K\\\spadesuit}$}.\quad 2: \fbox{$\color{black} {\substack{Q\\\spadesuit}}$},\fbox{$\color{red} {\substack{Q\\\heartsuit}}$}.\quad 3: \fbox{$\color{red} {\substack{10\\\heartsuit}}$},\fbox{$\substack{10\\\spadesuit}$}. \quad 4:\fbox{$\color{black} {\substack{A\\\spadesuit}}$},\fbox{$\color{blue}{\substack{A\\\diamondsuit}}$}.$$ Cards on the table: $$ \fbox{$\color{red} {\substack{5\\\heartsuit}}$}, \fbox{$\color{green} {\substack{10\\\clubsuit}}$}, \fbox{$\color{red} {\substack{A\\\heartsuit}}$},\fbox{$\color{blue} {\substack{Q\\\diamondsuit}}$},\fbox{$\color{blue} {\substack{J\\\diamondsuit}}$}.$$
