Consider 21 different pearls on a necklace. How many ways can the pearls be placed in on this necklace such that 3 specific pearls always remain together?

Explanation

After fixing the places of three pearls, treating 3 specific pearsl=1 units. So , we have now
18 pearls+1 unit=19 and the number of arrangement will be (19-1)!=18!
also, number of ways of 3 pearls can be arranged between themselves is 3!=6.
since, there is no distinction between the clockwise and anti-clockwise arrangement.
So, the required number of arrangements`=(1)/(2)18!*6(18!)`