Four men and four women (including two particular women, and ) are to be seated in a row so that no two men sit next to each other and , are not seated next to each other. The number of ways is

Answer and explanation

Correct answer: A. 2592

  1. Step 1: Seat the women first in a row in ways. This creates available gaps (ends and between women) to seat the men such that no two men are adjacent.
  2. Step 2: Choose and arrange men in of these gaps in ways. The total number of arrangements with no two men adjacent is .
  3. Step 3: Subtract the forbidden cases where and sit next to each other. Treat or as a single block ( arrangements of women units), creating gaps for men. The men must fill all gaps with no man between and in ways, giving invalid arrangements. Thus, valid ways .
Answer
2592.

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