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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. plz answer and explain
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3 ladies and 3 gents can be seated at a round table so that any two an...
G1 L1L2 G2 sath me rhege ... (3-1)!they 2 ladies n 2 gents arrange them self in. ...2! × 2!n other G3 n L3 arrange them self in 3 ways each ....sooo final ans .... (3-1)!2!2!3.3=72
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3 ladies and 3 gents can be seated at a round table so that any two an...
Solution:
Possible arrangements:
First, let's seat the gentlemen:
- There are 3 gentlemen, so there are 3 choices for the first seat.
- After one gentleman is seated, there are 2 choices for the next seat, then 1 choice for the last seat.
- Therefore, there are 3 x 2 x 1 = 6 ways to seat the gentlemen.
Next, let's seat the ladies:
- There are 3 ladies, so there are 3 choices for the first seat.
- We must seat the ladies such that any two and only two of them sit together.
- There are two cases to consider:
Case 1: Two ladies sit together, and the third lady sits apart.
- There are 3 ways to choose which two ladies sit together.
- There are 2 ways to choose which of the two adjacent seats the pair of ladies sit in.
- There are 2 ways to choose which of the remaining seats the third lady sits in.
- There are 2 ways to arrange the two ladies within their two adjacent seats.
- There are 2 ways to arrange the other lady in her seat.
- Therefore, there are 3 x 2 x 2 x 2 = 24 arrangements in this case.
Case 2: All three ladies sit together.
- There are 3 ways to choose which of the three adjacent seats the ladies sit in.
- There are 2 ways to arrange the ladies within their three adjacent seats.
- Therefore, there are 3 x 2 = 6 arrangements in this case.
Total number of arrangements:
- By the multiplication principle, the total number of arrangements is the product of the number of arrangements for each group of people.
- Therefore, the total number of arrangements is 6 x (24 + 6) = 180.
Answer: The number of ways to seat 3 ladies and 3 gentlemen at a round table such that any two and only two of the ladies sit together is 180.
Possible arrangements:
First, let's seat the gentlemen:
- There are 3 gentlemen, so there are 3 choices for the first seat.
- After one gentleman is seated, there are 2 choices for the next seat, then 1 choice for the last seat.
- Therefore, there are 3 x 2 x 1 = 6 ways to seat the gentlemen.
Next, let's seat the ladies:
- There are 3 ladies, so there are 3 choices for the first seat.
- We must seat the ladies such that any two and only two of them sit together.
- There are two cases to consider:
Case 1: Two ladies sit together, and the third lady sits apart.
- There are 3 ways to choose which two ladies sit together.
- There are 2 ways to choose which of the two adjacent seats the pair of ladies sit in.
- There are 2 ways to choose which of the remaining seats the third lady sits in.
- There are 2 ways to arrange the two ladies within their two adjacent seats.
- There are 2 ways to arrange the other lady in her seat.
- Therefore, there are 3 x 2 x 2 x 2 = 24 arrangements in this case.
Case 2: All three ladies sit together.
- There are 3 ways to choose which of the three adjacent seats the ladies sit in.
- There are 2 ways to arrange the ladies within their three adjacent seats.
- Therefore, there are 3 x 2 = 6 arrangements in this case.
Total number of arrangements:
- By the multiplication principle, the total number of arrangements is the product of the number of arrangements for each group of people.
- Therefore, the total number of arrangements is 6 x (24 + 6) = 180.
Answer: The number of ways to seat 3 ladies and 3 gentlemen at a round table such that any two and only two of the ladies sit together is 180.
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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. plz answer and explain
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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. plz answer and explain for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant 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. plz answer and explain covers all topics & solutions for Quant 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. plz answer and explain.
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. plz answer and explain for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant 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. plz answer and explain covers all topics & solutions for Quant 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. plz answer and explain.
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