8 chairs are placed at the sides of a long table in such a w

8 chairs are placed at the sides of a long table in such a way that three are 4 chairs on the left and 4 chairs on the right. 8 children are to be seated on these chairs. If 2 specific children want to sit on the same side, calculate the number of ways all the 8 children can be seated.

Solution

Let the two sides of the long table be A and B.

Two children who wish to sit on the same side (say, side A) can be accommodated in two chairs in either of the sides in [2*^4P_2] ways. Now six children are left who can sit on six chairs on both the sides of the table in 6! ways.

Hence, the total number of ways in which 8 children can be seated

= [2*^4P_2 * 6!]

= [(2*4!*6!)/((4-2)!)]

= 17280

=>answer.