Question

In a playground, $3$ sisters and $5$ other girls are playing together. The number of ways in which all the girls be seated in a circular order so that the three sisters are not seated together is

• A. $5040$
• B. $4920$
• C. $4320$
• D. $2160$

Answer 1

The correct option is C $4320$

There are $3$ sisters and $5$ other girls in total of $8$ girls. The number of ways to arrange these $8$ girls in a circular manner $=(8-1)!=7!$.
The number of ways when sisters always come together in the arrangement $=5!\times 3!.$
$($Consider three sisters as one unit$)$

Hence, the required number of ways in which the arrangement can take place if none of the $3$ sisters are seated together:
$=7!-(5!\times 3!)$
$=5040-(120\times 6)$
$=5040-720=4320.$