$$\begin{gathered}  n\left( S \right) = 5! = 120 \hfill \\  n\left( A \right) = 24 \to P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( S \right)}} = \frac{{24}}{{120}} = \frac{1}{5} \hfill \\ \end{gathered} $$