Algorithm to select a single, random combination of values?

Robert Floyd invented a sampling algorithm for just such situations. It's generally superior to shuffling then grabbing the first x elements. As originally written it assumes values from 1..N, but it's trivial to produce 0..N, and/or use non-contiguous values by simply treating the values it produces as subscripts into a vector/array/whatever.

In pseuocode, the algorithm runs like this (stealing from Jon Bentley's Programming Pearls column "A sample of Brilliance").

initialize set S to empty
for J := N-M + 1 to N do
    T := RandInt(1, J)
    if T is not in S then
        insert T in S
    else
        insert J in S

That last bit (inserting J if T is already in S) is the tricky part, but the bottom line is that it assures precisely the correct mathematical probability of inserting J, so it produces correct, unbiased results.