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?

Solution:

Let us consider M = Men; W = Women.

There are 4 women and 5 men.

We have to place women in even place, so our arrangement would look like this:

M W M W M W M W M

Using factorials,

• No. of ways of arranging women among themselves = 4!
• No. of ways of arranging men among themselves = 5!

By fundamental principle of counting,

The total number of ways = 4! × 5! = 24 × 120 = 2880

NCERT Solutions Class 11 Maths Chapter 7 Exercise ME Question 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?

Summary:

If it is required to seat 5 men and 4 women in a row so that the women occupy the even places, then the possible number of such arrangements is 2880