Question

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?

• A. 2880
• B. 2480
• C. 3680
• D. 3280
• E. None of these

Answer 1

The correct option is A 2880

Total number of candidates = 5 + 4 = 9. In the row of 9 positions, the even places are 2nd, 4th, 6th and 8th. Now, number of even places = 4. Number of women to occupy the even places = 4.
$\therefore$ Even places can be filled = P(4, 4) ways
Number of men = 5
$\therefore$ The remaining 5 places can be filled by 5 men = P(5, 5) ways
$\therefore$ By the fundamental principle of counting:
$\therefore$ The required number of seating arrangements
$=P(4,4)\times P(5,5)=4\times 5!$
$=24\times 120=2880.$