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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?
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3 ladies and 3 gents can be seated at a round table so that any two an...
Understanding the Seating Arrangement
To solve the problem of seating 3 ladies and 3 gents at a round table such that any two and only two of the ladies sit together, we need to analyze the arrangement carefully.
Step 1: Grouping the Ladies
- We can treat the two ladies who will sit together as a single unit or "block."
- The third lady will sit separately.
Step 2: Arranging the Groups
- Thus, we have the following groups to arrange: the "block" of 2 ladies, the 3rd lady, and the 3 gents.
- This gives us a total of 5 units to arrange: (Block), Lady 3, Gent 1, Gent 2, Gent 3.
Step 3: Circular Permutation
- In circular permutations, the number of ways to arrange n units is (n-1)!.
- Here, we have 5 units, so the arrangements are (5-1)! = 4! = 24 ways.
Step 4: Arranging the Ladies Within the Block
- The block can consist of 2 ladies, and they can sit in 2! = 2 ways.
- So, the total arrangements for the ladies within the block adds to 2.
Step 5: Total Arrangements Calculation
- Now, we calculate the total arrangements:
- Total arrangements = Arrangements of 5 units × Arrangements of ladies in the block
- Total arrangements = 24 × 2 = 48 ways.
Conclusion
The total number of ways to seat 3 ladies and 3 gents at a round table so that any two and only two of the ladies sit together is 48.
To solve the problem of seating 3 ladies and 3 gents at a round table such that any two and only two of the ladies sit together, we need to analyze the arrangement carefully.
Step 1: Grouping the Ladies
- We can treat the two ladies who will sit together as a single unit or "block."
- The third lady will sit separately.
Step 2: Arranging the Groups
- Thus, we have the following groups to arrange: the "block" of 2 ladies, the 3rd lady, and the 3 gents.
- This gives us a total of 5 units to arrange: (Block), Lady 3, Gent 1, Gent 2, Gent 3.
Step 3: Circular Permutation
- In circular permutations, the number of ways to arrange n units is (n-1)!.
- Here, we have 5 units, so the arrangements are (5-1)! = 4! = 24 ways.
Step 4: Arranging the Ladies Within the Block
- The block can consist of 2 ladies, and they can sit in 2! = 2 ways.
- So, the total arrangements for the ladies within the block adds to 2.
Step 5: Total Arrangements Calculation
- Now, we calculate the total arrangements:
- Total arrangements = Arrangements of 5 units × Arrangements of ladies in the block
- Total arrangements = 24 × 2 = 48 ways.
Conclusion
The total number of ways to seat 3 ladies and 3 gents at a round table so that any two and only two of the ladies sit together is 48.
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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?
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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? 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? 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?.
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? 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? 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?.
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