GATE 2023 CE (CE2) – Question 7
Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?
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Correct answer: (A) 16
Explanation
**Step 1: treat each couple as one block.** If every husband sits next to his wife, each couple occupies two adjacent chairs, so we arrange 3 blocks around the circle.
**Step 2: circular arrangements of 3 blocks.** Seating is defined only by relative positions, so the number of circular orders is $(3-1)!=2$.
**Step 3: inside each block.** The husband and wife can swap places, giving 2 ways per couple, so $2^3=8$ ways.
**Step 4: total.**
$$2\times8=\mathbf{16}.$$