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In how many ways 7 men and 7 women can be seated
around a round table such that no two women can
sit together ?
- a)
- b)7!×6!
- c)
- d)7!
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In how many ways 7 men and 7 women can be seatedaround a round table s...
Most Upvoted Answer
In how many ways 7 men and 7 women can be seatedaround a round table s...
Firstly arrange men, no. of ways to arrange 7 men in a round table= 6!
now, each woman will sit between two men. total space = 7 i.e M W M W M...
now, no. of ways to sit 7 women on 7 places= 7!
total no. of ways = 6! * 7! = 3628800
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In how many ways 7 men and 7 women can be seatedaround a round table s...
Understanding the Problem
We need to seat 7 men and 7 women around a round table such that no two women are seated next to each other.
Step 1: Arranging the Men
- Since the arrangement is circular, we can fix one man’s position to avoid identical arrangements due to rotation.
- The remaining 6 men can be arranged in 6! ways.
Step 2: Creating Spaces for Women
- After seating the 7 men, they create 7 gaps (or spaces) around the table where women can be seated.
- The arrangement looks like this: M _ M _ M _ M _ M _ M _ M (M represents men and _ represents gaps).
Step 3: Arranging the Women
- We need to select 7 out of these 7 available gaps to seat the women, ensuring that no two women are sitting together.
- The 7 women can be arranged in these selected gaps in 7! ways.
Final Calculation
- The total number of arrangements is the product of the arrangements of men and women:
- Total arrangements = Arrangements of men × Arrangements of women = 6! × 7!
Thus, the correct answer is option 'B' (7! × 6!).
Conclusion
In summary, by fixing one man and arranging the others, we ensured that women are placed in separate gaps created by them. The arrangement of men and the arrangement of women lead us to the final number of valid seating arrangements.
We need to seat 7 men and 7 women around a round table such that no two women are seated next to each other.
Step 1: Arranging the Men
- Since the arrangement is circular, we can fix one man’s position to avoid identical arrangements due to rotation.
- The remaining 6 men can be arranged in 6! ways.
Step 2: Creating Spaces for Women
- After seating the 7 men, they create 7 gaps (or spaces) around the table where women can be seated.
- The arrangement looks like this: M _ M _ M _ M _ M _ M _ M (M represents men and _ represents gaps).
Step 3: Arranging the Women
- We need to select 7 out of these 7 available gaps to seat the women, ensuring that no two women are sitting together.
- The 7 women can be arranged in these selected gaps in 7! ways.
Final Calculation
- The total number of arrangements is the product of the arrangements of men and women:
- Total arrangements = Arrangements of men × Arrangements of women = 6! × 7!
Thus, the correct answer is option 'B' (7! × 6!).
Conclusion
In summary, by fixing one man and arranging the others, we ensured that women are placed in separate gaps created by them. The arrangement of men and the arrangement of women lead us to the final number of valid seating arrangements.
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In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer?
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In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer?.
In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In how many ways 7 men and 7 women can be seatedaround a round table such that no two women cansit together ?a) b)7!×6!c)d)7!Correct answer is option 'B'. Can you explain this answer?.
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