Eighteen guests have to seated, half on each side of a long table. Four particular guests desire to

Question

Eighteen guests have to 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.

Professor PC Thomas Classes · Answer

One side have a total 9 seats, so 9 guests can be arranged on one side in ${ }^{9} P_{9}$ ways $=9$. Out of total 18,7 wish to be seated on particular sides. Remaining 11 can be seated in ${ }^{11} C_{5}$ ways. Since their are only 5 seats left after the 4 guests are seated on one side. So total no of ways required in which arrangements can be made $={ }^{11} C_{5} 	imes 9!	imes 9$ !\