Question

A necklace is to be made from 3 red, 2 black and 2 white beads. How many possible configurations are there?

Answer 1

`(7!)/(3!2!2!)=5040/(6xx2xx2)=210`

Explanation:

There are 7 beads. If all the beads were unique, there'd be `7! = 5040` ways to arrange the beads.

However, there are three groups of unique beads and within each group the beads are the same. And so we need to divide by the ways those groups can be interchanged (so that we get rid of duplicates). This gives:

`(7!)/(3!2!2!)=5040/(6xx2xx2)=210`