Sixteen persons are to be seated along two sides of a rectangular table with eight chairs on either side. Of these sixteen, Amit, Jaya, Rishi and Neetu with to sit on one side of the table, while Paresh and Sadashiv with to sit on the other, in how many ways can the arrangement be done?

there is a rectangular table and sixteen persons are to be seated on the sixteen chairs along two opposite sides of the table, eight chairs on either side. Among these sixteen persons four want to sit on the same side so we can select that side in two ways and as given in the question two other persons want to sit on the other side of the table.

Now after selecting the side for four persons we can arrange them on eight chairs in 8P4 ways, similarly other two persons on the opposite side can be arranged on eight chairs in 8P2 ways. Rest 10 persons can be arranged on remaining 10 chairs in 10! Ways. So the total no.of ways to arrange these 16 persons considering all the conditions = 8P4 x 8P2 x 10! x 2

 

 

Regards

Arun (askIITians forum expert)