SEAMO 2027 - Paper F - SET 03 - Self-study Question 3

Question 3

How many ways are there to arrange 6 girls and 15 boys to dance in a circle such that there are at least 2 boys between any 2 adjacent girls?

Counting convention: all dancers are distinct; rotations count as the same arrangement, while reflections count separately.

$15!/3!$
$15!/(3!\cdot12!)$
$15!\cdot3!/8!$
$15!\cdot8!/3!$
None of the above