Question

Twelve persons are to be arranged around two round tables such that one table can accommodate seven persons and another five persons only. The number of ways in which these $12$ persons can be arranged is

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

Answer 1

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

Seven persons can be selected for the first table in ${}^{12}{C}_7$ ways.
Now these seven persons can be arranged in $6!$ ways. The remaining five persons can be arranged on the second table in $4!$ ways.
Hence, total number of ways is ${}^{12}{C}_{5}6!4!$.