Question

A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish for sit on one particular side and two on the other side. In how many ways can they be seated ?

Answer 1

No of persons = 16

Condition on specific persons = 4 and 2 = 6

Remaining people = 16- 6 = 10

So lets fill 8 people on both sides first from these 10.

First side, we can select 4 out of 10.

${}^{10}{C}_4{\times }^6{C}_6$

Now we can arrange these 8 people on both sides in $8!\times 8!$ ways

Answer ${=}^{10}{C}_4{\times }^6{C}_6\times 8!\times 8!$