A tea party is arranged for 16 people along two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. Then the number of ways that they can be seated is

There are 8 chairs on each side of the table.

4 persons opted to sit on one side and 2 persons on the other side.

Remaining 10 persons are to be distributed to the 2 sides containing 4, 6 in $\frac{10!}{4!6!}={10}_{{\mathrm{C}}_4}$ ways.

After distributing 8 persons on each side the 2 groups can be arranged in $8!\times 8!$ ways.

 Numbers of ways $={10}_{{\mathrm{C}}_4}\times 8!\times 8! ={10}_{{\mathrm{C}}_4} {(8!)}^2$