Question

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

• A. $2520$
• B. $20160$
• C. $40320$
• D. none of these

Answer 1

Answer: (B)

$20160$

Answer 2

Let $A, B$ be the corresponding speakers. Without any restrictions the eight 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 $8 \,!$. Also number of ways in which $A$ speaks before $B$ is exactly same as the number of ways in which $B$ speaks before $A$. $\therefore$ the reqd. no. of ways $=\frac{1}{2}\left(8\,!\right)$ $=20160$