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Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right?
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Six Persons A, B, C, D, E and F to be seated at a circular table. In h...
Introduction:
In this problem, we need to find the number of ways to seat six persons (A, B, C, D, E, and F) at a circular table, while satisfying the given conditions. The conditions state that person A must always have either B or C on his right, and person B must always have either C or D on his right.
Approach:
To solve this problem, we can use the concept of circular permutations. We will consider the positions of persons A, B, and C as fixed, and then arrange the remaining three persons (D, E, and F) around the table.
Arranging A, B, and C:
Since person A must always have either B or C on his right, we have two cases to consider:
1. If B is on the right of A:
- A can be fixed at any position on the table.
- B can be fixed to the right of A in only one way.
- C can be fixed to the right of B in only one way.
- The remaining three persons (D, E, and F) can be arranged in 3! = 6 ways.
2. If C is on the right of A:
- A can be fixed at any position on the table.
- C can be fixed to the right of A in only one way.
- B can be fixed to the right of C in only one way.
- The remaining three persons (D, E, and F) can be arranged in 3! = 6 ways.
Therefore, the total number of ways to arrange A, B, and C = (1 + 1) * 6 = 12 ways.
Arranging D, E, and F:
After fixing the positions of A, B, and C, we are left with three persons (D, E, and F) to arrange around the table. Since the positions of these three persons are not fixed, we can arrange them in 3! = 6 ways.
Total number of arrangements:
The total number of ways to arrange all six persons at the circular table is the product of the number of ways to arrange A, B, and C, and the number of ways to arrange D, E, and F. Therefore, the total number of arrangements = 12 * 6 = 72 ways.
Conclusion:
In conclusion, there are 72 ways to seat six persons (A, B, C, D, E, and F) at a circular table, while satisfying the given conditions that person A must always have either B or C on his right, and person B must always have either C or D on his right.
In this problem, we need to find the number of ways to seat six persons (A, B, C, D, E, and F) at a circular table, while satisfying the given conditions. The conditions state that person A must always have either B or C on his right, and person B must always have either C or D on his right.
Approach:
To solve this problem, we can use the concept of circular permutations. We will consider the positions of persons A, B, and C as fixed, and then arrange the remaining three persons (D, E, and F) around the table.
Arranging A, B, and C:
Since person A must always have either B or C on his right, we have two cases to consider:
1. If B is on the right of A:
- A can be fixed at any position on the table.
- B can be fixed to the right of A in only one way.
- C can be fixed to the right of B in only one way.
- The remaining three persons (D, E, and F) can be arranged in 3! = 6 ways.
2. If C is on the right of A:
- A can be fixed at any position on the table.
- C can be fixed to the right of A in only one way.
- B can be fixed to the right of C in only one way.
- The remaining three persons (D, E, and F) can be arranged in 3! = 6 ways.
Therefore, the total number of ways to arrange A, B, and C = (1 + 1) * 6 = 12 ways.
Arranging D, E, and F:
After fixing the positions of A, B, and C, we are left with three persons (D, E, and F) to arrange around the table. Since the positions of these three persons are not fixed, we can arrange them in 3! = 6 ways.
Total number of arrangements:
The total number of ways to arrange all six persons at the circular table is the product of the number of ways to arrange A, B, and C, and the number of ways to arrange D, E, and F. Therefore, the total number of arrangements = 12 * 6 = 72 ways.
Conclusion:
In conclusion, there are 72 ways to seat six persons (A, B, C, D, E, and F) at a circular table, while satisfying the given conditions that person A must always have either B or C on his right, and person B must always have either C or D on his right.
Community Answer
Six Persons A, B, C, D, E and F to be seated at a circular table. In h...
Correct option is A)
Say B on right side of A
D or C will be right of B
This can be done in 2! ways. Remaining three places can be filled in 3! ways
=2!×3!=12 ways.
Say C on right of A
B can be filled in 3 places. (B next should be D).
B immediately next is D
′A′,′C′,′B′,′D′ are filled in 3 ways. Remaining two places in 2 ways.
Total =6 ways
Total number =12+6=18 ways.
Say B on right side of A
D or C will be right of B
This can be done in 2! ways. Remaining three places can be filled in 3! ways
=2!×3!=12 ways.
Say C on right of A
B can be filled in 3 places. (B next should be D).
B immediately next is D
′A′,′C′,′B′,′D′ are filled in 3 ways. Remaining two places in 2 ways.
Total =6 ways
Total number =12+6=18 ways.
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Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right?
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Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right?.
Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right?.
Solutions for Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? in English & in Hindi are available as part of our courses for CA Foundation.
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Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right?, a detailed solution for Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? has been provided alongside types of Six Persons A, B, C, D, E and F to be seated at a circular table. In how many ways can this be done, if A (b) 8 (c) 24 (d) None of these must always have either B or C on his right and B must always have either C or D on his right? theory, EduRev gives you an
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