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What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?
- a)4
- b)3
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
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What is the ratio of number of arrangements of 9 people sitting around...
Problem:
What is the ratio of the number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side in both cases?
Solution:
In order to solve this problem, we need to calculate the number of arrangements for each case and then find their ratio.
Arrangements around an Isosceles Triangular Table:
In the case of an isosceles triangular table, we have 9 people to arrange. Let's assume that one person is fixed at the top of the triangle. Now, we have 8 people to arrange around the remaining two sides of the triangle.
Since the table is isosceles, the two sides have the same number of seats. Therefore, we can calculate the number of arrangements as follows:
Number of arrangements = (Number of ways to arrange 8 people around a circle) / 2
The number of ways to arrange 8 people around a circle is given by (8-1)! = 7!.
Therefore, the number of arrangements around an isosceles triangular table is 7!.
Arrangements around an Equilateral Triangular Table:
In the case of an equilateral triangular table with 3 people sitting on each side, we have 9 people to arrange. Let's assume that one person is fixed at the top of the triangle. Now, we have 8 people to arrange around the remaining sides of the triangle.
Since the table is equilateral, all three sides have the same number of seats. Therefore, we can calculate the number of arrangements as follows:
Number of arrangements = (Number of ways to arrange 8 people around a circle) / 3
The number of ways to arrange 8 people around a circle is given by (8-1)! = 7!.
Therefore, the number of arrangements around an equilateral triangular table is 7!.
Calculating the Ratio:
Now, we need to calculate the ratio of the number of arrangements around an isosceles triangular table to the number of arrangements around an equilateral triangular table.
Ratio = (Number of arrangements around an isosceles triangular table) / (Number of arrangements around an equilateral triangular table)
Ratio = (7!) / (7!) = 1
Therefore, the ratio of the number of arrangements of 9 people sitting around an isosceles triangular table to the number of arrangements of 9 people sitting around an equilateral triangular table is 1.
Answer:
The correct answer is option 'c) 1'.
What is the ratio of the number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side in both cases?
Solution:
In order to solve this problem, we need to calculate the number of arrangements for each case and then find their ratio.
Arrangements around an Isosceles Triangular Table:
In the case of an isosceles triangular table, we have 9 people to arrange. Let's assume that one person is fixed at the top of the triangle. Now, we have 8 people to arrange around the remaining two sides of the triangle.
Since the table is isosceles, the two sides have the same number of seats. Therefore, we can calculate the number of arrangements as follows:
Number of arrangements = (Number of ways to arrange 8 people around a circle) / 2
The number of ways to arrange 8 people around a circle is given by (8-1)! = 7!.
Therefore, the number of arrangements around an isosceles triangular table is 7!.
Arrangements around an Equilateral Triangular Table:
In the case of an equilateral triangular table with 3 people sitting on each side, we have 9 people to arrange. Let's assume that one person is fixed at the top of the triangle. Now, we have 8 people to arrange around the remaining sides of the triangle.
Since the table is equilateral, all three sides have the same number of seats. Therefore, we can calculate the number of arrangements as follows:
Number of arrangements = (Number of ways to arrange 8 people around a circle) / 3
The number of ways to arrange 8 people around a circle is given by (8-1)! = 7!.
Therefore, the number of arrangements around an equilateral triangular table is 7!.
Calculating the Ratio:
Now, we need to calculate the ratio of the number of arrangements around an isosceles triangular table to the number of arrangements around an equilateral triangular table.
Ratio = (Number of arrangements around an isosceles triangular table) / (Number of arrangements around an equilateral triangular table)
Ratio = (7!) / (7!) = 1
Therefore, the ratio of the number of arrangements of 9 people sitting around an isosceles triangular table to the number of arrangements of 9 people sitting around an equilateral triangular table is 1.
Answer:
The correct answer is option 'c) 1'.
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Community Answer
What is the ratio of number of arrangements of 9 people sitting around...
In the above equilateral triangle, A, D and G will get the same view from the table.
Similarly, B, E, H will get the same view and C, F, I will get the same view.
For A, the arrangement will be 8! and there are 3 different views.
So, total number of arrangements = 3*8!
In the above isosceles triangular arrangement, every member will get a different view.
That's why the total number of arrangements will be 9!
Ratio of number of arrangements of isosceles table to equilateral table will be
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What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?a)4b)3c)1d)2Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?a)4b)3c)1d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?a)4b)3c)1d)2Correct answer is option 'B'. Can you explain this answer?.
What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?a)4b)3c)1d)2Correct answer is option 'B'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?a)4b)3c)1d)2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the ratio of number of arrangements of 9 people sitting around an isosceles triangular table and the same 9 people sitting around an equilateral triangular table with 3 people sitting on each side if the table in both the cases?a)4b)3c)1d)2Correct answer is option 'B'. Can you explain this answer?.
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