Seven persons sit in a row at random. The probability that three persons A, B, C sit together in a particular order is

$$\begin{gathered} The number of ways of arrainging 7 boys among themselves is n\left(S\right)=7! \\ Let E be the event of having three persons A,B,C are together in a perticular order \end{gathered}$$   

$Take A,B,C as one bunch, the number of ways of arranging 5 things in 5! ways$

$n\left(E\right)=5!$

          $Therefore, the probability is P\left(E\right) =\frac{5!}{7!}$