Question

How many necklaces of 12 bead each, can be made from 18 beads of different colours?​

Answer 1

Answer:

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!

Answer 2

Answer:

In the case of necklace, there is no distinction between the clockwise and anticlockwise arrangements, then the required number of circular permutations

=

2×12

18

P

12

=

6!×2418!

=

18×17×16×15×14×13!/6×5×4×3×2×1×24

=

119×13!/2