A number of 18 guests have to be seated, half oneach side of a long table. Four particular guests desire to sit on oneparticular side and three others on the other side. Determine the number ofways in which the sitting arrangements can be made.

A number of 18 guests have to be seated, half oneach side of a long ta

1.	A number of 18 guests have to be seated, half oneach side of a long table. Four particular guests desire to sit on oneparticular side and three others on the other side. Determine the number ofways in which the sitting arrangements can be made.
Answer» Correct Answer - `""^(9)P_(4) xx ""^(9)P_(3)(11)!` Let the two sides be A and B. Assume that four particular guests wish to sit on side A. Four guests who wish to sit on side A can be accommodated on nine chairs in `""^(9)P_(4)` ways and three guests who wish to sit on side B can be accommodated in `""^(9)P_(3)` ways. Now, the remaining guests are left who can sit on 11 chairs on both sides of the table in `(11!)` ways. Hence, the total number of ways in which 18 persons can be seated `= ""^(9)P_(4) xx ""^(9)P_(3) xx (11)!.`

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A number of 18 guests have to be seated, half oneach side of a long table. Four particular guests desire to sit on oneparticular side and three others on the other side. Determine the number ofways in which the sitting arrangements can be made.

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