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4. 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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4. Eight guests have to be seated 4 on each side of a long rectangular...
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.
To find: The number of ways in which the sitting arrangements can be made.
We can divide this problem into two cases:
Case 1: Two particular guests sit on the same side of the table.
In this case, we have to select 2 guests out of 8 to sit on one side of the table, which can be done in 8C2 ways. The remaining 6 guests can be seated on the other side of the table in 6! ways. Also, we can arrange the two groups of guests in 2! ways.
Therefore, the total number of ways in which the sitting arrangements can be made in this case is:
8C2 × 6! × 2! = 201,600
Case 2: Two particular guests sit on opposite sides of the table.
In this case, we have to select 2 guests out of 8 to sit on one side of the table, which can be done in 8C2 ways. The remaining 6 guests can be seated on the other side of the table in 6! ways. Also, we can arrange the two groups of guests in 2! ways.
Out of the 3 remaining guests, we have to select 2 to sit on the same side of the table as the 2 particular guests. This can be done in 3C2 ways. The selected guests can be arranged in 2! ways.
Therefore, the total number of ways in which the sitting arrangements can be made in this case is:
8C2 × 6! × 2! × 3C2 × 2! = 483,840
Total number of ways = Case 1 + Case 2 = 201,600 + 483,840 = 685,440
Hence, the correct option is (d) 1278.
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.
To find: The number of ways in which the sitting arrangements can be made.
We can divide this problem into two cases:
Case 1: Two particular guests sit on the same side of the table.
In this case, we have to select 2 guests out of 8 to sit on one side of the table, which can be done in 8C2 ways. The remaining 6 guests can be seated on the other side of the table in 6! ways. Also, we can arrange the two groups of guests in 2! ways.
Therefore, the total number of ways in which the sitting arrangements can be made in this case is:
8C2 × 6! × 2! = 201,600
Case 2: Two particular guests sit on opposite sides of the table.
In this case, we have to select 2 guests out of 8 to sit on one side of the table, which can be done in 8C2 ways. The remaining 6 guests can be seated on the other side of the table in 6! ways. Also, we can arrange the two groups of guests in 2! ways.
Out of the 3 remaining guests, we have to select 2 to sit on the same side of the table as the 2 particular guests. This can be done in 3C2 ways. The selected guests can be arranged in 2! ways.
Therefore, the total number of ways in which the sitting arrangements can be made in this case is:
8C2 × 6! × 2! × 3C2 × 2! = 483,840
Total number of ways = Case 1 + Case 2 = 201,600 + 483,840 = 685,440
Hence, the correct option is (d) 1278.
Community Answer
4. Eight guests have to be seated 4 on each side of a long rectangular...
3C1 × 4! × 4! = 1728
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4. 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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4. 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 4. 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 4. 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.?.
4. 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 4. 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 4. 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.?.
Solutions for 4. 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.? in English & in Hindi are available as part of our courses for CA Foundation.
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4. 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 4. 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 4. 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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