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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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