Question

Twelve persons are to be arranged around two round tables such that one table can accommodate seven persons and another five persons only. Answer the given question.

Number of ways in which these $12$ persons can be arranged is?

• A. ${}^{12}{C}_{5}7!5!$
• B. $6!4!$
• C. ${}^{12}{C}_{5}6!4!$
• D. None of these

Answer 1

The correct option is C ${}^{12}{C}_{5}6!4!$

No. of ways of arranging $12$ people around two round tables that can accommodate $7$ people in one and $5$ in other is first select $5$ people to be accommodated in the table of $5$ ${12}_{C_5}$.

No. of ways of arranging n people circularly is $(n-1)!$

so, in ${12}_{C_5}6!4!$ ways $12$ people can be accommodated.