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Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.
1. E is sitting opposite to H.
2. B is second to the right of E.
3. G and H are to the left of A.
4. C is sitting opposite to G.
How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.
- a)2
- b)4
- c)6
- d)8
- e)9
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Eight friends are sitting around a circular table. The names of the fr...
Solution: Let E and H sit at seats 1 and 5. So, B is at 7.
A can be at 2, 3 or 4. So, G can be at 3, 4 or 6 depending on A’s position.
So, from (4), (i) C can be at 8 and G at 4 (ii) C can be at 2 and G at 6 Consider (i) C can be at 8 and G at 4 Case I: A is at 2.
D and F can sit at remaining positions in 2 ways. Case II: A is at 3.
D and F can sit at remaining positions in 2 ways.
Thus, 4 arrangements are possible.
As above, we get 4 possible arrangements if C can be at 2 and Gat 6.
Thus, 8 arrangements are possible.
Hence, option 4.
A can be at 2, 3 or 4. So, G can be at 3, 4 or 6 depending on A’s position.
So, from (4), (i) C can be at 8 and G at 4 (ii) C can be at 2 and G at 6 Consider (i) C can be at 8 and G at 4 Case I: A is at 2.
D and F can sit at remaining positions in 2 ways. Case II: A is at 3.
D and F can sit at remaining positions in 2 ways.
Thus, 4 arrangements are possible.
As above, we get 4 possible arrangements if C can be at 2 and Gat 6.
Thus, 8 arrangements are possible.
Hence, option 4.
Most Upvoted Answer
Eight friends are sitting around a circular table. The names of the fr...
Understanding the Problem
To solve the seating arrangement problem, we begin by using the clues provided to establish the positions of each friend around the table.
Clue Analysis
- E is sitting opposite to H.
This means if E is in one position, H is directly across from E.
- B is second to the right of E.
This indicates that if we know E's position, B can be easily placed.
- G and H are to the left of A.
This implies that A must be seated such that G and H are positioned counterclockwise from A.
- C is sitting opposite to G.
Similar to E and H, this gives us another direct relationship between positions.
Setting Up the Arrangement
1. Fix E and H:
Assume E occupies position 1; thus, H is in position 5.
2. Position B:
B, being second to the right of E, would be in position 3.
3. Position A:
Since G and H must be to the left of A, A can only occupy positions 2, 4, 6, or 8.
4. Position G and C:
Depending on A's position, G will take one of the remaining positions, and C will sit opposite G.
Counting Arrangements
- After determining A's position, you can arrange G and C accordingly.
- Each position of A allows for distinct arrangements of G and C, resulting in different configurations.
Conclusion
By exploring A's possible positions, you can find 4 valid seating arrangements that meet all conditions. Thus, the answer is:
Answer: 8 different seating arrangements possible.
To solve the seating arrangement problem, we begin by using the clues provided to establish the positions of each friend around the table.
Clue Analysis
- E is sitting opposite to H.
This means if E is in one position, H is directly across from E.
- B is second to the right of E.
This indicates that if we know E's position, B can be easily placed.
- G and H are to the left of A.
This implies that A must be seated such that G and H are positioned counterclockwise from A.
- C is sitting opposite to G.
Similar to E and H, this gives us another direct relationship between positions.
Setting Up the Arrangement
1. Fix E and H:
Assume E occupies position 1; thus, H is in position 5.
2. Position B:
B, being second to the right of E, would be in position 3.
3. Position A:
Since G and H must be to the left of A, A can only occupy positions 2, 4, 6, or 8.
4. Position G and C:
Depending on A's position, G will take one of the remaining positions, and C will sit opposite G.
Counting Arrangements
- After determining A's position, you can arrange G and C accordingly.
- Each position of A allows for distinct arrangements of G and C, resulting in different configurations.
Conclusion
By exploring A's possible positions, you can find 4 valid seating arrangements that meet all conditions. Thus, the answer is:
Answer: 8 different seating arrangements possible.
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Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer?.
Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer?.
Solutions for Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for UPSC.
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Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Eight friends are sitting around a circular table. The names of the friends are A, B, C, D, E, F, G, and H.1. E is sitting opposite to H.2. B is second to the right of E.3. G and H are to the left of A.4. C is sitting opposite to G.How many different sitting arrangements are possible?Note: If seats were numbered 1 to 8 in clockwise order, then 2, 3 and 4 would have been to the left of 1 and also to the right of 5.a)2b)4c)6d)8e)9Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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