Question

The number of ways in which 5 men, 5 women and 12 children can sit around a circular table so that the children are always together is:

• A. $4!4!12!$
• B. $11!12!$
• C. $10!12!$
• D. $(12!{)}^2$

Answer 1

The correct option is C $10!12!$

As children are always to be seated together, they can be considered as a single element with number of arrangements possible among themselves $=12!$
Total no of elements $=5M+5W+1C=11$
No. of arrangements around a circular table $=(n-1)!=10!$
$\therefore$ Total no. of ways $=10!12!$