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.

Explanation

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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