JEE Class main Answered

Since three specific beads always together in the necklace, let us consider these three beads as single item.

Remaining 20 beads and the three specific beads are 21 items .

If these 2 items arranged in circular ring , then  these beads are arranged in  20! ways.

For each arrangment of 20! ways, three beads can be arranged in 3! ways .

Hence total number of arrangement is  ( 20! 3 ! )

If we consider clockwise and anticlockwise arrangements are same then ,

total number of ways of arranging the beads is  ( 20 ! 3 ! ) /2