GATE CE 2023 Set 2 — Question 7
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
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?
Correct answer
(A) 16
Solution
1.Treat each of the three husband-wife pairs as a single unit. Let the pairs be , , and .
2.There are 3 units to be arranged around a circular table. The number of ways to arrange distinct objects in a circle is . For , the number of ways is .
3.Within each unit, the husband and wife can be seated in 2 different ways (Husband-Wife or Wife-Husband). Since there are 3 such units, the total number of internal arrangements is .
4.The total number of seating arrangements is the product of the circular arrangements of the units and the internal arrangements within the units: .
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