Houjun Liu


A permutation \(\pi\) of some \(\{1,2,…, n\}\) is a rearrangement of this list. There are \(n!\) different permutations of this set.

A permutation is an ORDERED arrangement of objects.

permutation with indistinct objects

What if you want to order a set with sub-set of indistinct objects? Like, for instance, how many ways are there to order:

\begin{equation} 10100 \end{equation}

For every permutation of \(1\) in this set, there are two copies being overcounted.

Let there are \(n\) objects. \(n_1\) objects are the indistinct, \(n_2\) objects are indistinct, … \(n_{r}\) objects are the same. The number of permutations are:

\begin{equation} \frac{n!}{{n_1}!{n_2}! \dots {n_r}!} \end{equation}

You can use iterators to give you permutations.