# all possible combinations

Duncan Smith buzzard at urubu.freeserve.co.uk
Wed Jul 13 17:52:42 CEST 2005

```rbt wrote:
> On Wed, 2005-07-13 at 10:21 -0400, rbt wrote:
>
>>Say I have a list that has 3 letters in it:
>>
>>['a', 'b', 'c']
>>
>>I want to print all the possible 4 digit combinations of those 3
>>letters:
>>
>>4^3 = 64
>>
>>aaaa
>>abaa
>>aaba
>>aaab
>>acaa
>>aaca
>>aaac
>>...
>>
>>What is the most efficient way to do this?
>
>
> Expanding this to 4^4 (256) to test the random.sample function produces
> interesting results. It never finds more than 24 combinations out of the
> possible 256. This leads to the question... how 'random' is sample ;)
>
> Try it for yourselves:
>
> test = list('1234')
>
> combinations = []
> while 1:
>     combo = random.sample(test, 4)
>     possibility = ''.join(combo)
>     if possibility not in combinations:
>         print possibility
>         combinations.append(possibility)
>         continue
>     else:
>         continue
>

There are only 24 possible lists that random.sample(test, 4) can return,
corresponding to the 24 possible orderings of 4 items.  i.e.
random.sample() samples without replacement.  You need to sample with
replacement.

Duncan

```