Question

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

• A. $24\times 8!\times 8!$
• B. $(8!{)}^3$
• C. $210\times 8!\times 8!$
• D. $16!$

Answer 1

The correct option is C $210\times 8!\times 8!$

At first, we will arrange seats for those $6$ persons who wants to sit in a specific row.

We have remaining $10$ persons to arrange now.and out of $10$ people we select $6$ people to sit on this side where $6$ seats are empty

The total arrangements will be $={}^{10}{C}_4$

The remaining $4$ people will automatically placed in those $4$ seats available on other side

The total arrangements will be $=1$

And now all the 16 people ar placed in their seats according to the constraints, now we have to arrange them in both sides individually $8!\times 8!$

Total possible arrangements will be $={}^{10}{C}_4\times 1\times 8!\times 8!$

$=210\times 8!\times 8!$