GATE CE 2024 Set 1 — Question 7
Go beyond PYQs with Success TrackerAI-powered personalised practice and doubt support. Unlimited practice on eligible plans; AI usage limits apply.MCQ+2 / -0.67HardPermutations & CombinationsQuantitative AptitudeGeneral Aptitude
General Aptitude → Quantitative Aptitude → Permutations & Combinations
Last updated
Question
Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defined by the relative positions of the people.How many unique seating arrangements are possible such that each person is sitting next to their twin?
Correct answer
(A) 12
Solution
Let the three sets of twins be represented as blocks , , and . Since there are 8 identical chairs and 6 people, there are 2 empty chairs, which can be treated as two identical blocks and .We need to arrange these 5 blocks around a circular table. The blocks are: , , , , and .The number of circular permutations of items where some are identical is given by Polya's Enumeration Theorem or by considering linear permutations and dividing by the number of rotations.Total linear permutations of is .Since the greatest common divisor of the counts of each type of block (1, 1, 1, 2) is 1, there are no periodic arrangements. Thus, the number of unique circular arrangements is simply the total linear permutations divided by the number of positions:Therefore, there are 12 unique seating arrangements.
Continue learning with Success Tracker
A step still unclear? Work through it with support
Use Success Tracker to ask about the reasoning, then try another GATE CE question to check your understanding.
AI-powered practice· Unlimited practice on eligible plans
- PYQs with solutions
- Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
- Practice that adapts
- Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
- AI doubt support
- Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.
Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.
This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.
More questions on Quantitative Aptitude
2026 Set 2 Q1'The team ____ more than 300 runs in 20 overs ____ rains. However, some players needed to…2026 Set 1 Q1‘The shopkeeper sells lemons.’ In this sentence, the word ‘lemons’ is the ________.2026 Set 2 Q2If a positive real satisfies the following equation then…2026 Set 1 Q2The figure below is supposed to show three non-overlapping shapes – one oval and two triangles.…2026 Set 2 Q3The next figure (indicated by ‘?’) in the sequence is