CA Foundation Exam > CA Foundation Questions > 3 ladies and 3 gents can be seated at a round...
Start Learning for Free
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these?
Most Upvoted Answer
3 ladies and 3 gents can be seated at a round table so that any two an...
Given:
- There are 3 ladies and 3 gents.
- They need to be seated at a round table.
- Any two and only two of the ladies sit together.
To find:
The number of ways the 3 ladies and 3 gents can be seated at a round table.
Solution:
We can solve this problem using permutation and combination.
Step 1: Fix the positions of the ladies
Since any two and only two of the ladies sit together, we can fix the positions of the ladies in the following ways:
- LLG, where L represents a lady and G represents a gent.
- LGL
- GLL
Step 2: Arrange the gents
Now that we have fixed the positions of the ladies, we can arrange the gents in the remaining positions. Since the table is round, the arrangement of the gents is essentially a circular arrangement.
Step 3: Calculate the number of ways
To calculate the number of ways, we need to consider the arrangements for each case where the positions of the ladies are fixed.
Case 1: LLG
In this case, we can arrange the gents in 2! = 2 ways.
Case 2: LGL
Again, we can arrange the gents in 2! = 2 ways.
Case 3: GLL
Once more, we can arrange the gents in 2! = 2 ways.
Total number of ways:
Since the positions of the ladies can be fixed in 3 ways and the gents can be arranged in 2 ways for each case, the total number of ways is 3 * 2 = 6.
Answer:
The number of ways the 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together is 6. Therefore, the correct option is (d) none of these.
- There are 3 ladies and 3 gents.
- They need to be seated at a round table.
- Any two and only two of the ladies sit together.
To find:
The number of ways the 3 ladies and 3 gents can be seated at a round table.
Solution:
We can solve this problem using permutation and combination.
Step 1: Fix the positions of the ladies
Since any two and only two of the ladies sit together, we can fix the positions of the ladies in the following ways:
- LLG, where L represents a lady and G represents a gent.
- LGL
- GLL
Step 2: Arrange the gents
Now that we have fixed the positions of the ladies, we can arrange the gents in the remaining positions. Since the table is round, the arrangement of the gents is essentially a circular arrangement.
Step 3: Calculate the number of ways
To calculate the number of ways, we need to consider the arrangements for each case where the positions of the ladies are fixed.
Case 1: LLG
In this case, we can arrange the gents in 2! = 2 ways.
Case 2: LGL
Again, we can arrange the gents in 2! = 2 ways.
Case 3: GLL
Once more, we can arrange the gents in 2! = 2 ways.
Total number of ways:
Since the positions of the ladies can be fixed in 3 ways and the gents can be arranged in 2 ways for each case, the total number of ways is 3 * 2 = 6.
Answer:
The number of ways the 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together is 6. Therefore, the correct option is (d) none of these.
Community Answer
3 ladies and 3 gents can be seated at a round table so that any two an...
2 × 3! × 3! = 72
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these?
Question Description
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these?.
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these?.
Solutions for 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? defined & explained in the simplest way possible. Besides giving the explanation of
3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these?, a detailed solution for 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? has been provided alongside types of 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? theory, EduRev gives you an
ample number of questions to practice 3 ladies and 3 gents can be seated at a round table so that any two and only two of the ladies sit together. The number of ways is (a) 70 (b) 27 (c) 72 (d) none of these? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup