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

The correct option is B $20160$

Let $A,B,C,D,E,F,G,H$ be eight speaker,

Now, considering B should speak only after A.

we have,

$\to$ A at first place, then other can be arranged in $7!$ ways

$\to$ A at second, B can be placed after A in $(7!-6!)$ ways

$\to$ A at third, B can be arranged in $(7!-2\times 6!)$ ways

and so on

Therefore, Total ways $7\times 7!-21\times 6!$

$=35280-15120=20160$