# Fast generation of permutations

Paul Rubin http
Sat Jan 28 11:07:34 EST 2006

```"Anton Vredegoor" <anton.vredegoor at gmail.com> writes:
> >     def deals():
> >         for i in xrange(13**5):
> >             cards = [(i//p) % 13 for p in (1, 13, 169, 2197, 28561)]
> >             yield cards
>
> This gives hands like [0,0,0,0,1] and [0,0,0,1,0] which are
> permutations of one another.

Yes, that's intentional, I thought the idea was to figure out the
probability of each type of poker hand, which means you have to
count those multiple occurrences.

> Below is a piece of code that avoids this.

Nice.

> Another hand, for example [0,0,1,2,3], would allow only 384 colorings,...
> Similar things happen for other partionings of the hands into numbers...
>
> This is very fascinating. Maybe someday I'll make a tkinter script with
> a visual tree structure allowing all kinds of numbers of "cards", and
> arbitrary numbers of variables to partition by.

Cool, I'd still like to know why (13**5)-13 = C(52,5) other than
by just doing the arithmetic and comparing the results.  Maybe your
tkinter script can show that.

```