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CA Foundation · Quantitative Aptitude · Permutations and Combinations

Five men and five women are to be seated around a circular table so that no two men sit together, that is, men and women alternate. In how many ways can this be done?

The answer is 2880. Seat the five women around the table in 4! = 24 ways, which creates five gaps between them. The five men can then be placed in these gaps in 5! = 120 ways, giving 24 × 120 = 2880 arrangements.

  1. A2880Correct
  2. B14400
  3. C5760
  4. D720

Explanation

Seat the 5 women first around the circle: (5-1)! = 24 ways. This creates 5 gaps between the women, and the 5 men can fill them in 5! = 120 ways. Total = 24 × 120 = 2880. The value 14400 is 5! × 5! = 120 × 120, which wrongly treats the first group as seated in a row.

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