Question

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, In how many ways can they be seated?

Answer 1

The four persons who wish to occupy side A can be accommodated on eight chairs in
${}^8{P}_4=\frac{8!}{4!}=8\times 7\times 6\times 5$ ways.
The two persons who wish to occupy side B can be accommodated on eight chairs in
${}^8{P}_2=\frac{8!}{6!}=8\times 7$ ways.