Permutation: Bracelet

How to solve a bracelet permutation: formula, 1 example, and its solution.

Formula

Formula

The number of ways
to arrange n things in a bracelet is
(n - 1)!/2.

This is the bracelet permutation formula.

The bracelet permutation formula
is similar to
the circular permutation formula: (n - 1)!.

But a bracelet can be flipped.
So 2 is divided.

Example

Example

Solution

There are 7 beads.
These are used to make a bracelet.

This is arranging 7 beads
in a bracelet.

So the number of the ways is,
7 - 1,
6!
over 2.

6! = 6⋅5⋅4⋅3⋅2⋅1

Factorial

Cancel 2⋅1 in the numerator
and cancel 2 in the denominator.

6⋅5 = 30
4⋅3 = 12

30⋅12 = 360

So 360 is the answer.