Algorithm: combinations of (k) taken from (n) values

[Matthew Hirsch]

Hi All,

Onto the next question...

Can anyone think of an algorithm to store as lists all possible 
combinations of k numbers taken from n possible numbers.  For example, 
given 5 values, I want to choose 2.  The number of possible combinations 
is given by 5!/(3!2!)=10.  They are:

[0,1], [1,2], [2,3], [3,4]
[0,2], [1,3], [2,4]
[0,3], [1,4]
[0,4]

I have something like:

n=5

for first_choice in range(n):
   for second_choice in range(first_choice+1,n):
      for third_choice in range(second_choice+1,n):
         print first_choice, second_choice, third_choice


The problem is that I'll be dealing with large combinations of numbers 
and it doesn't make sense to continue writing nested for loops.  I'm 
trying to figure out something that generates all combinations, just 
based on values of k and n.  Any ideas?

Thanks for your help,
Matt