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

Answer» 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`


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