JEE Exam > JEE Questions > Five men and four women are to be seated on 9...
Start Learning for Free
Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.
- a)43200
- b)42100
- c)39560
- d)6! x 4!
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Five men and four women are to be seated on 9 adjacent seats in a cine...
Given: Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together.
To solve this problem, we can use the principle of permutations and combinations.
Step 1: We can first arrange the five men in 5! ways.
Step 2: Now, we need to arrange the four women in such a way that no two women sit together. To do this, we can think of the women as 'dividers' between the men. We have 6 gaps between the men where we can place these dividers so that no two women sit together. This is because if we place all four women in one gap, then two of them will sit together. Therefore, we need to choose 4 gaps from the 6 gaps available and arrange the women in these gaps.
Number of ways to choose 4 gaps from 6 gaps = 6C4 = 15
Number of ways to arrange the four women in these gaps = 4!
Therefore, total number of ways to arrange the five men and four women = 5! x 15 x 4! = 43,200
Hence, option A is the correct answer.
To solve this problem, we can use the principle of permutations and combinations.
Step 1: We can first arrange the five men in 5! ways.
Step 2: Now, we need to arrange the four women in such a way that no two women sit together. To do this, we can think of the women as 'dividers' between the men. We have 6 gaps between the men where we can place these dividers so that no two women sit together. This is because if we place all four women in one gap, then two of them will sit together. Therefore, we need to choose 4 gaps from the 6 gaps available and arrange the women in these gaps.
Number of ways to choose 4 gaps from 6 gaps = 6C4 = 15
Number of ways to arrange the four women in these gaps = 4!
Therefore, total number of ways to arrange the five men and four women = 5! x 15 x 4! = 43,200
Hence, option A is the correct answer.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer?
Question Description
Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. 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 Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer?.
Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. 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 Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer?.
Solutions for Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. 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 Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Five men and four women are to be seated on 9 adjacent seats in a cinema hall in such a way that no two women sit together. Find the number of ways in which they can be arranged.a)43200b)42100c)39560d)6! x 4!Correct answer is option 'A'. 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