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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?
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Eight guests have to be seated 4 on each side of a long rectangular ta...
Number of Ways to Seat Guests at a Rectangular Table
There are 8 guests who need to be seated at a long rectangular table with 4 guests on each side. Two particular guests want to sit on one side, while three others want to sit on the other side. Let's calculate the number of ways in which the seating arrangements can be made.

Step 1: Arrange the Two Particular Guests
- The two particular guests can be seated in 2! = 2 ways on one side of the table.

Step 2: Arrange the Remaining Guests
- After seating the two particular guests, we are left with 6 guests to be seated on the opposite side.
- The 6 guests can be arranged in 6! = 720 ways.

Step 3: Divide by the Number of Ways to Seat the Remaining Guests
- The 6 remaining guests can be arranged in 2 ways on the opposite side of the table.
- Therefore, the number of ways to seat the remaining guests is 720 / 2 = 360 ways.

Step 4: Multiply the Number of Ways for Each Step
- The total number of ways to seat the guests is the product of the number of ways to seat the particular guests and the number of ways to seat the remaining guests.
- Total number of ways = 2 * 360 = 720 ways.
Therefore, there are 720 ways in which the seating arrangements can be made for the 8 guests at the rectangular table according to the specified conditions.
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Read the following information and answer the itemthat follow.A leading socialite decided to organise a dinner and invited a few of her friends. Only the host and the hostess were sitting at the opposite ends of a rectangular table, with three persons along each side. The pre-requisite for the seating arrangement was that each person must be seated such that at least on one side it has a person of the opposite sex. Maqbool is opposite Shobha, who is not the hostess. Ratan has a woman on his right and is sitting opposite a woman. Monisha is sitting to the hostesss right, next to Dhirubhai. One person is seated between Madhuri and Urmila, who is not the hostess. The men were Maqbool, Ratan, Dhirubhai and Jackie, while the women were Madhuri, Urmila, Shobha and Monisha.Q.If Ratan would have exchanged sets with a person four places to his left, which ofthe following would have been true after the exchange?I. No one was seated between two persons of the opposite sex. (e.g. no man was seated between two women)II. One side of the table consisted entirely of persons of the same sex.III. Either the host or the hostess changed seates.

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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?
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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? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC 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? covers all topics & solutions for UPSC 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?.
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