I am trying to figure out how many ways 20 beads can be placed around a necklace, but i'm not really sure where to start.
Could someone give me a hint on this?
my thought is that it is 20! / 20
If we arrange twenty persons around a circular table, that can be done in
$\displaystyle 19!$ ways.
But with beads on a necklace we can view it from two sides.
That is to say if we had three beads: red, green, & blue.
There would be only one necklace.
$\displaystyle \begin{array}{*{20}c}
{} & {red} & {} \\
{blue} & {} & {green} \\ \end{array} $ is the same as $\displaystyle \begin{array}{*{20}c}
{} & {red} & {} \\
{green} & {} & {blue} \\ \end{array} $