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The number of ways in which 7 men be seated at a round table so that two particular men are not side by side is
- a)2400
- b)120
- c)360
- d)480
Correct answer is option 'D'. Can you explain this answer?
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The number of ways in which 7 men be seated at a round table so that t...
6! – 5! x 2 = 480
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The number of ways in which 7 men be seated at a round table so that t...
Understanding the Problem
To determine the number of ways to seat 7 men at a round table such that two particular men (let’s call them A and B) are not seated next to each other, we can follow a systematic approach.
Total Arrangements Without Restrictions
- For n people seated at a round table, the formula is (n-1)!.
- Here, n = 7, so the total arrangements without restrictions = 6! = 720.
Arrangements Where A and B are Together
- Treat A and B as a single unit or block.
- This block can be arranged in 2 ways (AB or BA).
- Now, we have 6 units to arrange (the block + 5 other men).
- The arrangements = (6-1)! = 5! = 120.
- Therefore, the total arrangements where A and B are together = 120 * 2 = 240.
Calculating Arrangements Where A and B are Not Together
- To find the arrangements where A and B are not seated together, subtract the arrangements where they are together from the total arrangements.
- Arrangements where A and B are not together = Total arrangements - Arrangements where A and B are together.
- This gives us 720 - 240 = 480.
Conclusion
Thus, the number of ways to seat 7 men at a round table such that two particular men are not side by side is 480. Therefore, the correct option is D.
To determine the number of ways to seat 7 men at a round table such that two particular men (let’s call them A and B) are not seated next to each other, we can follow a systematic approach.
Total Arrangements Without Restrictions
- For n people seated at a round table, the formula is (n-1)!.
- Here, n = 7, so the total arrangements without restrictions = 6! = 720.
Arrangements Where A and B are Together
- Treat A and B as a single unit or block.
- This block can be arranged in 2 ways (AB or BA).
- Now, we have 6 units to arrange (the block + 5 other men).
- The arrangements = (6-1)! = 5! = 120.
- Therefore, the total arrangements where A and B are together = 120 * 2 = 240.
Calculating Arrangements Where A and B are Not Together
- To find the arrangements where A and B are not seated together, subtract the arrangements where they are together from the total arrangements.
- Arrangements where A and B are not together = Total arrangements - Arrangements where A and B are together.
- This gives us 720 - 240 = 480.
Conclusion
Thus, the number of ways to seat 7 men at a round table such that two particular men are not side by side is 480. Therefore, the correct option is D.
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The number of ways in which 7 men be seated at a round table so that two particular men are not side by side isa)2400b)120c)360d)480Correct answer is option 'D'. Can you explain this answer?
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