Question

A teaparty is arranged for 16 people along two sides of a large table with 8 chairs on each side. Four men want to sit on one particular side and two on the other side. The number of ways in which they can be seated is

• A. $\frac{6!\,8!\,10!}{4!\,6!}$
• B. $\frac{8!\,8!\,10!}{4!\,6!}$
• C. $\frac{8!\,8!\,6!}{6!\,4!}$
• D. None of these

Answer 1

Answer: (B)

$\frac{8!\,8!\,10!}{4!\,6!}$

Answer 2

There are 8 chairs on each side of the table. Let the sides be represented by A and B. Let four persons sit on side A, then number of ways of arranging 4 persons on 8 chairs on side $A = ^8P_4$ and then two persons sit on side B. The number of ways of arranging 2 persons on 8 chairs on side $B = ^8P_2$ and the remaining 10 persons can be arranged in remaining 10 chairs in 10! ways. Hence the total number of ways in which the persons can be arranged $=^{8}P_{4}\times^{8}P_{2}\times10!=\frac{8!\,8!\,10!}{4!\,6!}$