91影视

There are eight songs to make eight different playlists.

The number of different ways in which r units can be arranged in r number of places is $r!$.

The factorial can be elaborated as follows:

$r!=r脳\left(r-1\right)脳\left(r-2\right)脳...脳1$

There is a total of eight songs.

The number of ways in which eight songs can be arranged to form a playlist is

$$\begin{gathered} 8!=8脳7脳6脳5脳4脳3脳2脳1 \\ =40320 \end{gathered}$$

Therefore, the number of possible eight-song playlists is 40320.

The total number of playlists possible is 40320.

The number of ways of forming a playlist with songs arranged according to the alphabetical order of their title is 1.

The probability thatthe songs are arranged in the alphabetical order of their title is

$$\begin{gathered} P\left(\text{songs}\text{arranged}\text{in}\text{alphabetical}\text{order}\right)=\frac{\text{Number}\text{of}\text{favourable}\text{ways}}{\text{Total}\text{number}\text{of}\text{ways}} \\ =\frac{1}{40320} \end{gathered}$$

Therefore,the probability that the songs are arranged in the alphabetical order of their title is.