# Permutation: Bracelet

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

## 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.

## ExampleBeads → Bracelet

Solution

Solution (Detail)

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.