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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?

1. 16
2. 4
3. 120
4. 720

Correct answer: 16

Solution

Glue each husband-wife pair into a block. Three blocks around a circle give (3-1)!=2 arrangements, and each pair can be ordered 2 ways: 2*2^3=16. Stored answer 4 is wrong; correct is 16.

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