Question 42 of 42intermediate🔧 ApplyNumerical3 marks

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?

Correct Answer

2880 arrangements

Exercise: Miscellaneous Exercise on Chapter 6 | Q: 9 | (Chapter: 24)
For More Understanding

Explanation

This question is similar to Example 24 from the textbook context, which demonstrates the approach of first arranging one group and then placing the other group in specific positions. Here, we identify even and odd positions in a row of 9 seats, then arrange women and men separately in their designated positions using the multiplication principle.

Solution Steps

  1. Step 1: Total number of persons = 5 men + 4 women = 9 persons. In a row of 9 positions, even places are positions 2, 4, 6, 8 (4 places) and odd places are positions 1, 3, 5, 7, 9 (5 places).

  2. Step 2: Since 4 women must occupy the 4 even places, the number of ways to arrange 4 women in 4 even places = 4! = 24 ways.

  3. Step 3: The 5 men must occupy the remaining 5 odd places. The number of ways to arrange 5 men in 5 odd places = 5! = 120 ways.

  4. Step 4: By multiplication principle, total number of arrangements = 4! × 5! = 24×12024 \times 120 = 2880 arrangements.

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