Question

In how many ways can 5 men and 3 women be seated in a row such that no two women sit adjacent?

• A. 720
• B. 2400
• C. 1440
• D. 14400

Hint:

To ensure that no two women sit adjacent, arrange the men first and then place the women in the available spaces between them.

Answer 1

The Correct Option is D

To arrange the men, we have \(5!\) ways. The women must sit in the spaces between the men, and there are \(6\) available spaces. We need to select \(3\) spaces from these \(6\), which can be done in \(\binom{6}{3} = 20\) ways. Then, the \(3\) women can be arranged in the selected spaces in \(3!\) ways. Thus, the total number of arrangements is: \[ 5! \times \binom{6}{3} \times 3! = 120 \times 20 \times 6 = 14400 \]