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

Out of 18 guests half, i.e., 9 to be seated on side A and rest 9 on side B.
Now out of 18 guests, 4 particular guests desire to sit on one paritcular side say side A and other 3 on other side B.
From rest of 11 guests have to select 5 more for side A. This can be done in `.^(11)C_(5)` ways. The remaining 6 guests will sit on side B. Now 9 guest on each side can be arranged in 9! says.
So, total number arrangements are `.^(11)C_(5)xx9!xx9!`.