How to calculate how many different ways I can order a list in python

Question

I'm a little confused on how to do this, and I know it probably requires a bit of probability knowledge too (which I'm lacking).

How can I calculate how many ways, and also get all the possibilities, of how many ways I can order a list?

For example if I have lst = ["a", "a", "a", "a", "b", "b", "b"], how many ways can I order this/how can I get all the possible combinations? I've been looking through itertools but haven't found something for it.

Answer 1

You can use permutations() to get the all permutations, and set() in order to remove the duplicate items:

>>> from itertools import permutations
>>> set(permutations(lst))
{('b', 'a', 'b', 'a', 'a', 'a', 'b'), ('b', 'a', 'a', 'b', 'a', 'a', 'b'), ('b', 'a', 'a', 'b', 'b', 'a', 'a'), ('a', 'a', 'b', 'b', 'a', 'a', 'b'), ('a', 'a', 'b', 'a', 'b', 'b', 'a'), ('b', 'b', 'a', 'b', 'a', 'a', 'a'), ('b', 'a', 'a', 'a', 'b', 'a', 'b'), ('b', 'a', 'b', 'a', 'b', 'a', 'a'), ('b', 'b', 'a', 'a', 'b', 'a', 'a'), ('b', 'b', 'b', 'a', 'a', 'a', 'a'), ('a', 'a', 'a', 'b', 'a', 'b', 'b'), ('a', 'a', 'b', 'b', 'b', 'a', 'a'), ('a', 'a', 'a', 'b', 'b', 'b', 'a'), ('a', 'b', 'b', 'a', 'a', 'b', 'a'), ('b', 'a', 'b', 'b', 'a', 'a', 'a'), ('a', 'b', 'b', 'b', 'a', 'a', 'a'), ('a', 'b', 'a', 'a', 'a', 'b', 'b'), ('a', 'b', 'a', 'b', 'a', 'b', 'a'), ('a', 'b', 'b', 'a', 'a', 'a', 'b'), ('a', 'b', 'b', 'a', 'b', 'a', 'a'), ('a', 'a', 'b', 'a', 'b', 'a', 'b'), ('a', 'b', 'a', 'b', 'b', 'a', 'a'), ('b', 'b', 'a', 'a', 'a', 'b', 'a'), ('a', 'a', 'b', 'a', 'a', 'b', 'b'), ('a', 'a', 'a', 'a', 'b', 'b', 'b'), ('b', 'a', 'b', 'a', 'a', 'b', 'a'), ('b', 'b', 'a', 'a', 'a', 'a', 'b'), ('a', 'b', 'a', 'a', 'b', 'b', 'a'), ('b', 'a', 'a', 'b', 'a', 'b', 'a'), ('a', 'a', 'a', 'b', 'b', 'a', 'b'), ('a', 'b', 'a', 'a', 'b', 'a', 'b'), ('a', 'a', 'b', 'b', 'a', 'b', 'a'), ('a', 'b', 'a', 'b', 'a', 'a', 'b'), ('b', 'a', 'a', 'a', 'a', 'b', 'b'), ('b', 'a', 'a', 'a', 'b', 'b', 'a')}
>>> 

Note that his approach is not an optimized way, since it calculates all the permutations first, although it returns an iterator and doesn't store all of them in memory but still it's not the best way it's just good if you are dealing with non-large data sets.

If you want to use an optimized way you can customize the permutations's equivalent function which has mentioned in documentation.