auto-generating form value permutations..

id like to create a script that runs through a form, and autogenerates
every single permutation for every single value, as well as option.
The task is because I am currently working on a webservice project
where I am feeding in nightly a set of values from an external data
source, and populating my form with those values. In the end, I end up
resending a new query to this datasource with a custom url, including
as parameters the values chosen. Sooooo, the end goal would be to have
one massive array which I can see all of the various URL's that get
created for the user.

I hate bleek descriptions, so heres a little visual:

element1 => selectbox('opt1','opt2','opt3')
element2 => textbox('val1')
element3 => multipleselect('multopt1' through 'multoptN')

so, a simple forloop on the 1st option within the first selectbox as
my primary choice could produce several values.. here would be 2
permutations:

values[] = arr('opt1','val1','multopt10');
values[] =
arr('opt1','val1',array('multopt10','multiopt33','multiopt34 '));

and then in the end( not what I am concerned about, but just to
complete the example):

URL://?selectboxid=opt1&textboxid=val1&multipleselectid=mult iiopt10
-or-
URL://?selectboxid=opt1&textboxid=val1&multipleselectid[]=mu ltiiopt10
&multipleselectid[]=multiiopt33&multipleselectid[]=multiiopt 34

conceptually, i just can't think how to approach this.

ideas?