Question
Download Solution PDF"m" men and "n" women are to be seated in a row so that no two women sit together. If m > n, then
number of ways in which they can be seated, is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe Correct answer is Option 3.
Key Points⇔ Arrange the men: There are m! ways to arrange the m men.
⇔ Gaps for women: After arranging the men, there are m + 1 gaps available for placing the women.
⇔ Choose gaps for women: We need to select n gaps out of m + 1 gaps. This can be done in (m+1) / n ways.
⇔Arrange the women: The n women can be arranged in n! ways in the selected gaps.
Total number of ways: = m! * ( m +1 / n ) * n !
Which simplifies to:
Final Answer:\(\frac{\lfloor m \mid m+1}{\lfloor m-n+1}\)
Last updated on May 9, 2025
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