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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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After seating 4 on one side and 3 on the other side, we have to select out of 11,5 on one side and 6 on the other side.
Now, remaining selecting of one half side ` = ""^((18 - 4 - 3))C_(5) = ""^(11)C_(5)`
and the other half side `""^((11 - 5))C_(6) = ""^(6)C_(6)`
Total arrangements `= ""^(11)C_(5) xx 9"!" xx ""^(6)C_(6) xx 9"!"`
`= (11"!")/(5"!"6"!") xx 9"!" xx 1 xx 9"!"`
`= (11"!")/(5"!"6"!") xx 9"!" xx 9"!"`
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