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Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.?
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Eight guests have to be seated 4 on each side of a long rectangular ta...
Solution:
Given, 8 guests have to be seated 4 on each side of a long rectangular table.
Two particular guests desire to sit on one side of the table and 3 on the other side.
Let us consider the two particular guests as A and B, and the remaining guests as C, D, E, F, G, and H.
Now, A and B have to sit on one side of the table, and the remaining three guests have to sit on the other side.
The number of ways in which A and B can be seated on one side of the table is 2! = 2.
The number of ways in which the remaining three guests can be seated on the other side of the table is 3! = 6.
Now, we have to arrange the remaining 3 guests on the other side of the table.
The number of ways in which 3 guests can be seated on one side of a rectangular table is (3-1)! = 2.
Therefore, the total number of ways in which the seating arrangements can be made is 2 x 6 x 2 = 24.
Since there are two identical sides of the table, the total number of ways in which the seating arrangements can be made is 24/2 = 12.
Hence, the correct answer is option (d) 1278.
Note: It is important to break down the problem into smaller parts and use the concept of permutation and combination to arrive at the solution. Also, it is necessary to consider all the given conditions while solving the problem.
Given, 8 guests have to be seated 4 on each side of a long rectangular table.
Two particular guests desire to sit on one side of the table and 3 on the other side.
Let us consider the two particular guests as A and B, and the remaining guests as C, D, E, F, G, and H.
Now, A and B have to sit on one side of the table, and the remaining three guests have to sit on the other side.
The number of ways in which A and B can be seated on one side of the table is 2! = 2.
The number of ways in which the remaining three guests can be seated on the other side of the table is 3! = 6.
Now, we have to arrange the remaining 3 guests on the other side of the table.
The number of ways in which 3 guests can be seated on one side of a rectangular table is (3-1)! = 2.
Therefore, the total number of ways in which the seating arrangements can be made is 2 x 6 x 2 = 24.
Since there are two identical sides of the table, the total number of ways in which the seating arrangements can be made is 24/2 = 12.
Hence, the correct answer is option (d) 1278.
Note: It is important to break down the problem into smaller parts and use the concept of permutation and combination to arrive at the solution. Also, it is necessary to consider all the given conditions while solving the problem.
Community Answer
Eight guests have to be seated 4 on each side of a long rectangular ta...
3c1×4!×4!= 1728
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Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.?
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Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.? 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 long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.? 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 long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.?.
Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.? 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 long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.? 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 long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.?.
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Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.?, a detailed solution for Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.? has been provided alongside types of Eight guests have to be seated 4 on each side of a long rectangular table.2 particular guests desire to sit 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 (a) 1732 (b) 1728 (c) 1730 (d) 1278.? theory, EduRev gives you an
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