CA Foundation · Quantitative Aptitude · Seating Arrangements
Four married couples are to sit around a circular table so that every husband sits next to his wife. In how many different ways can the eight people be seated if only relative positions matter and rotations are counted as the same arrangement?
The number of arrangements is 96. Treating each couple as a block, four blocks can sit around a circular table in 3! = 6 ways. Each couple can be ordered internally in 2 ways, so 2 to the power 4 equals 16, and 6 times 16 gives 96.
- A48
- B144
- C96Correct
- D384
Explanation
Treat each couple as one unit. Four units around a circle can be arranged in (4 - 1)! = 6 ways. Within each couple the two people can swap places in 2 ways, giving 2^4 = 16. Total = 6 × 16 = 96. The figure 384 comes from wrongly using 4! instead of 3! for the circular arrangement.
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