If eight persons are to address a meeting then the number of ways in which a specified speaker is to speak before another specified speaker, is 

Let $A$ and $B$ be the corresponding speakers. Without any restriction, the $8$ persons can be arranged among themselves in $8!$ ways, but the number of ways in which $A$ speaks before $B$ and the number of ways in which $B$ speaks before $A$ make up this $8!$. Also the number of ways in which $A$ speaks before $B$ is exactly same as the number of ways $B$ speaks before $A$.