Misc 9
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
There are total 9 people
Since women occupy even places
Places 2, 4, 6, 8 will be occupied by women
And Rest will be occupied by men
The seating arrangement will be follows
Now, we have to arrange 5 women and 4 men
Arrangements of 4 women
4 women can sit in 4 positions
Total number of ways
= 4P4
= 4!/(4 − 4)!
= 4!/0! = 4!/1 = 4 × 3 × 2 × 1
= 24 ways
Arrangements of 5 men
5 men can sit in 5 positions
Total number of ways
= 5P5
= 5!/(5 − 5)!
= 5!/0! = 5!/1 = 5 × 4 × 3 × 2 × 1
= 120
Thus,
Total number of arrangements = 24 × 120
= 2880

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.