\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A coach selects two players at random from a group of four players, labeled A, B, C, and D, without replacement (once a player is chosen, they are not available for the next selection). The table below shows all possible outcomes for selecting Player 1 and Player 2, where an "X" indicates an impossible outcome due to the same player being selected twice.
\(\begin{aligned} & \textcolor{colorprop}{\text{Player 2}} \\ \textcolor{colordef}{\text{Player 1}} \end{aligned} \) \(\textcolor{colorprop}{A}\) \(\textcolor{colorprop}{B}\) \(\textcolor{colorprop}{C}\) \(\textcolor{colorprop}{D}\)
\(\textcolor{colordef}{A}\) X \(\textcolor{colordef}{A}\textcolor{colorprop}{B}\) \(\textcolor{colordef}{A}\textcolor{colorprop}{C}\) \(\textcolor{colordef}{A}\textcolor{colorprop}{D}\)
\(\textcolor{colordef}{B}\) \(\textcolor{colordef}{B}\textcolor{colorprop}{A}\) X \(\textcolor{colordef}{B}\textcolor{colorprop}{C}\) \(\textcolor{colordef}{B}\textcolor{colorprop}{D}\)
\(\textcolor{colordef}{C}\) \(\textcolor{colordef}{C}\textcolor{colorprop}{A}\) \(\textcolor{colordef}{C}\textcolor{colorprop}{B}\) X \(\textcolor{colordef}{C}\textcolor{colorprop}{D}\)
\(\textcolor{colordef}{D}\) \(\textcolor{colordef}{D}\textcolor{colorprop}{A}\) \(\textcolor{colordef}{D}\textcolor{colorprop}{B}\) \(\textcolor{colordef}{D}\textcolor{colorprop}{C}\) X
Calculate the probability that player C is selected as either Player 1 or Player 2, simplifying the fraction.
\(P(\text{"selecting player C"}) =\)