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Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is?
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Eight guests have to be seated 4 on each side of a rectangular table, ...
Understanding the Seating Arrangement
To solve the problem of seating 8 guests at a rectangular table with specific preferences, we need to account for the guests' desires regarding their seating sides.
Guests' Preferences
- 2 Particular Guests: They want to sit on one side of the table.
- 3 Other Guests: They prefer to sit on the opposite side.
Total Guests and Arrangement
- Total guests = 8
- Guests on each side = 4
- Side A (with 2 particular guests) will have 2 more guests.
- Side B (with 3 other guests) will have 1 more guest.
Seating Arrangements Calculation
1. Choose Remaining Guests:
- Choose 2 guests for Side A from the remaining 6 (8 total - 2 specific).
- The number of ways to choose 2 guests = 6C2 = 15.
2. Arrange Guests on Side A:
- Once selected, the arrangement for 4 guests on Side A (2 specific + 2 chosen) = 4! = 24 ways.
3. Arrange Guests on Side B:
- The remaining 4 guests will automatically go to Side B.
- The arrangement for these 4 guests = 4! = 24 ways.
Total Arrangements
The total number of arrangements is calculated by multiplying the combinations and arrangements:
- Total Arrangements = (Number of ways to choose guests for Side A) x (Arrangements for Side A) x (Arrangements for Side B)
- Total Arrangements = 15 x 24 x 24 = 8640.
Conclusion
Thus, the total number of ways in which the seating arrangements can be made is 8640.
To solve the problem of seating 8 guests at a rectangular table with specific preferences, we need to account for the guests' desires regarding their seating sides.
Guests' Preferences
- 2 Particular Guests: They want to sit on one side of the table.
- 3 Other Guests: They prefer to sit on the opposite side.
Total Guests and Arrangement
- Total guests = 8
- Guests on each side = 4
- Side A (with 2 particular guests) will have 2 more guests.
- Side B (with 3 other guests) will have 1 more guest.
Seating Arrangements Calculation
1. Choose Remaining Guests:
- Choose 2 guests for Side A from the remaining 6 (8 total - 2 specific).
- The number of ways to choose 2 guests = 6C2 = 15.
2. Arrange Guests on Side A:
- Once selected, the arrangement for 4 guests on Side A (2 specific + 2 chosen) = 4! = 24 ways.
3. Arrange Guests on Side B:
- The remaining 4 guests will automatically go to Side B.
- The arrangement for these 4 guests = 4! = 24 ways.
Total Arrangements
The total number of arrangements is calculated by multiplying the combinations and arrangements:
- Total Arrangements = (Number of ways to choose guests for Side A) x (Arrangements for Side A) x (Arrangements for Side B)
- Total Arrangements = 15 x 24 x 24 = 8640.
Conclusion
Thus, the total number of ways in which the seating arrangements can be made is 8640.
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Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is?
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Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made 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 Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is?.
Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made 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 Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Eight guests have to be seated 4 on each side of a rectangular table, 2 particular guest desires to on one side of the table and 3 on the other side.. The number of ways in which the sitting arrangements can be made is?.
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