CA Foundation · Quantitative Aptitude · Seating Arrangements
Four men and four women are to be seated around a circular table so that no two men sit together and no two women sit together. In how many ways can this be done?
The answer is 144. Arrange the four men in a circle in 3! = 6 ways, then place the four women in the four gaps between them in 4! = 24 ways. The product 6 × 24 gives 144 alternating arrangements.
- A24
- B72
- C144Correct
- D576
Explanation
Seat the 4 men around the table first: (4-1)! = 6 ways. This creates 4 gaps between them, and the 4 women can occupy these gaps in 4! = 24 ways. Total = 6 × 24 = 144. The value 576 wrongly uses 4! for the men as well, ignoring that circular rotations are identical.
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