It is required to seat 5 men and 3 women in a row so that the women occupy the even places. How many such arrangements are possible?
To find: number of arrangements in which women sit in even places
Condition: women occupy even places
Here the total number of people is 8.
In this question first, the arrangement of women is required.
The positions where women can be made to sit is 2nd, 4th, 6th, 8th. There are 4 even places in which 3 women are to be arranged.
Women can be placed in P (4,3) ways. The rest 5 men can be arranged in 5! ways.
Therefore, the total number of arrangements is P (4,3) ×5!
Formula:
Number of permutations of n distinct objects among r different places, where repetition is not allowed, is
P(n,r) = n!/(n-r)!
Therefore, a permutation of 4 different objects in 3 places and the arrangement of 5 men are
P (4,3) ×5! = 
= 
= 2880.
Hence number of ways in which they can be seated is 2880.