First slide

Permutations

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

Moderate

A

40320
B

2520
C

20160
D

None of these

Solution

Let A, B be the corresponding speakers. Without any restriction 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.
$∴$ the required number of ways $= \frac{1}{2} (8!) = 20160$ .

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