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A number of 18 guests have to be seated,...

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

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As four particular gusts have seated on one side, so remaining five on that side can be selected out of eleven, ` is ^11C_5 `ways.
Since seven particular guests already desire to sit either of the sides. So we have remaining guests to sit either side of the table. Thus nine guests can be arranged in 9! ways.
Similarly, on another side, out of nine guests have seated so remaining six on that side can be selected out of six `is ^6C_6 `ways .
Thus nine guests can be arranged in 9! ways.
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Eighteen guest have to be sated. Half on each side of long table. Four particlular guest desire to sit on one particular side and three others on the other side. Determine the number of ways in which seating arrangements can be made.

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Knowledge Check

  • Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side. Determine the number of ways in which the sitting, arrangements can be made.

    A
    a. `18!`
    B
    b. `462 xx (9!)^2`
    C
    c. `(9!)^2`
    D
    d. `7!""xx (9!)^2`

  • Eighteen guests have to be seated half on each side of a long table. Four particle guests desire to sit on one particular side and three others on other side. Determine the number of ways in which the sitting, arrangements can be made.

    A
    `18!`
    B
    `462 xx (9!)^2`
    C
    `(9!)^2`
    D
    `7 xx (9!)^2`

  • Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. The number of sitting arrangements is

    A
    `""^(11)C_(7)(9!)^(2)`
    B
    `""^(11)C_(5)(9!)^(2)`
    C
    `7*(9!)^(2)`
    D
    `10!9!`

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