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.
- - - - - -
1 2 3 4 5 6 7 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! = \(\frac{4!}{(4-3)}\)5!
= \(\frac{24}{1}\) x 120
= 2880.
Hence number of ways in which they can be seated is 2880.
