JEE Exam > JEE Questions > The number of ways in which 6 men and 5 women...
Start Learning for Free
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]
- a)7! × 5!
- b)6! × 5!
- c)30!
- d)5! × 4!
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of ways in which 6 men and 5 women can dine at a round tabl...
No. of ways in which 6 men can be arranged at a round table = (6 - 1)! = 5!
Now women can be arranged in 6 P5 = 6! Ways.
Total Number of ways = 6! × 5!
Now women can be arranged in 6 P5 = 6! Ways.
Total Number of ways = 6! × 5!
Most Upvoted Answer
The number of ways in which 6 men and 5 women can dine at a round tabl...
We can use the concept of circular permutations to solve this problem. Since the table is round, we can fix one person (say a man) at one position and arrange the rest of the people around him. This can be done in (10-1)! = 9! ways.
Now, we need to ensure that no two women sit together. We can first arrange the 6 men in the 6 available seats, which can be done in 6! ways. Then, we can insert the 5 women in the 7 available gaps between the men, such that no two women sit together. This can be done in the following way:
_M_M_M_M_M_M_
We have 7 gaps (marked by underscores) where we can insert the women. We can choose 5 of these gaps for the women in 7C5 = 21 ways. Once we have chosen the gaps, we can arrange the women in them in 5! ways. Therefore, the total number of ways in which the people can be seated is:
9! * 6! * 21 * 5! = 907,200
Therefore, the correct answer is (d) 907,200.
Now, we need to ensure that no two women sit together. We can first arrange the 6 men in the 6 available seats, which can be done in 6! ways. Then, we can insert the 5 women in the 7 available gaps between the men, such that no two women sit together. This can be done in the following way:
_M_M_M_M_M_M_
We have 7 gaps (marked by underscores) where we can insert the women. We can choose 5 of these gaps for the women in 7C5 = 21 ways. Once we have chosen the gaps, we can arrange the women in them in 5! ways. Therefore, the total number of ways in which the people can be seated is:
9! * 6! * 21 * 5! = 907,200
Therefore, the correct answer is (d) 907,200.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer?
Question Description
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!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 The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!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 The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer?.
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!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 The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!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 The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer?.
Solutions for The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by[2003]a)7! × 5!b)6! × 5!c)30!d)5! × 4!Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup