When things are arranged in a circle then number of permutations ( arrangements ) is calculated in the following way :
Since one of the objects is always fixed in its position so the total number of objects to be arranged gets reduced by 1.
So if total n objects are there then no of permutations will be
(1) when clockwise and anticlockwise permutations are counted different = (n-1)!
(2) when clockwise and anticlockwise are not counted different = (n-1)!/2