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Question #40569
The Question
Five married couples are to be seated around a circular table with identical chairs. In how many ways can they be seated such that men and women alternate, and no husband sits next to his own wife?
Options
- A.
312
- B.
384
- C.
1056
- D.
1560
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Specialist
Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.
Concepts Behind This Question
Circular Permutations Constraint|Derangements (Inclusion-Exclusion)|Complementary Counting
Why This Question Is Tricky
Common Mistakes
This question tests the classic Menage problem, combining the Gap Method for circular permutations with Inclusion-Exclusion for derangements.
The primary trap is complementary counting without accounting for the circular nature of the forbidden adjacencies, often leading students to use the incorrect linear coefficient (yielding 384).
The secondary trap tests circular symmetry: students often forget to fix one person to break the rotational invariance, incorrectly using for the men and arriving at 1560.
Another common error is assuming standard derangements (), ignoring that each person has two forbidden adjacent seats, leading to 1056.
Quick Facts About This Question
Question Information
| Subject | Mathematics |
| Chapter | Permutations and Combinations - Class 11 |
| Concept | Circular Permutations Constraint |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |