documentclass{article

usepackage{pgfplots}
usepackage{tikz}

begin{document}
begin{tikzpicture}[
declare function={p(k,n) = 1-((n!)/((n^(k))*((n-k)!)));}
                    ]
begin{axis}[axis lines=middle,
            xlabel=$k$, ylabel=$y$,
            ylabel style={anchor=south},
            xlabel style={anchor=west},
            ymax=1.2, xmax=12.5,
            domain=0:12.5, samples at={0,...,12},
            no markers
                    ]
addplot+ [ycomb, red, very thick] {p(x,2)}; % <----
end{axis}
end{tikzpicture}

end{document}}