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.

Options

A. `9!xx9!`
B. `""^(11)C_(5)xx9!xx9!`
C. `(11!)/(5!)xx9!xx9!`
D. `""^(11)C_(5)`

Explanation

Since four particular guests want to sit on a particular side A (say) and three others on the other side B (say). So, we are left with 11 guests out of which we choose 5 for side A in `""^(11)C_(5)` ways and the remaining 6 for side B in `""^(6)C_(6)` ways.
Hence, the number of selections for the two sides is `""^(11)C_(5)xx""^(6)C_(6)`.
Now, 9 persons on each side of the table can be arranged among themselves in 9! ways.
`:.` Total number of arrangements `""^(11)C_(5)xx""^(6)C_(6)xx9!xx9`