Question

The number of ways in which 15 students A1, A2, ... A15 can be ranked such that A4 is always above A8 is

Answer 1

HELLO DEAR,

When A8 is in 2nd position A4 can occupy only 1st.

When A8 is in 3rd position A4 can occupy only 1st or 2nd.

So,
the number of ways in which A4 and A8 can be arranged = 1 + 2 +.......+ 14

now , this is in the form of ap:
Whose first term a = 1 , common difference d = 1, n = 14 , l = 14
so, 1 + 2 +.......+ 14 = 14/2 * [1 + 14]
= 14*15/2

In the remaining 13 positions other students can be permuted in 13! ways.

Hence,
total number of ways = 13! * 14*15/2 = 15!/2


I HOPE ITS HELP YOU DEAR,
THANKS