Algorithm to convert combinations to bitstring

Limbic~Region has asked for the wisdom of the Perl Monks concerning the following question:

All,
The formula to determine the number of combinations (C) from a group of items (N) when choosing a fixed number of items at a time (K) is C = N! / K! * (N - K)!

So if I had a list of 5 items and I chose 2 at a time, I would have 10 combinations 120 / 2 * 6

ABCDE = AB, AC, AD, AE, BC, BD, BE, CD, CE, DE
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Assuming:

1. The total number of items N is known
2. The number at a time K is known
3. The number of combinations C is known
4. All items of N are unique
5. All items of N are in ascending order
6. Combinations will be generated as shown above (or the reverse as shown above)

It should be possible to use a bitstring the size of C to represent each combination. My question is what algorithm could I use to convert say 'CD' to 8 (or 7 if 0 based) and flip that bit. The converse algorithm (taking the bit and obtaining the combination) is not needed but feel free to have fun.

Cheers - L~R

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