How many necklaces of 12 beads can be made from 18 beads of various colours?

First, we can select 12 beads out of 18 beads in ¹⁸C₁₂ ways.
Now, these 12 beads can make a necklace in 11! / 2 ways as clockwise and anti-clockwise arrangements are same.
So, required number of ways = [ ¹⁸C₁₂ .11! ] / 2!
= [¹⁸C₆.11! ] / 2!
= [18 x 17 x 16 x 15 x 14 x 13 x 11! ] / [6 x 5 x 4 x 3 x 2 x 1 x 2!]
= [17 x 7 x 13! ] / 2!
= 119 x 13 !/ 2