Thanks to your having identified what I was after as "combinations of n things taken k at a time"; which just hadn't dawned on me, I went looking around in the guts of Algorithm::Combinatorics and translated his XS version of __next_combinations() to C, and arrived at:

#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#include "..\C\mytypes.h"

int nextCombination( U8 *tuple, int len_tuple, int max_n ) {
    int i, j;
    I32 offset = max_n - len_tuple;

    for( i = len_tuple; i >= 0; --i ) {
        I32 n = tuple[ i ];
        if( n < i + offset ) {
            tuple[ i ] = ++n;
            for( j = i + 1; j <= len_tuple; ++j ) tuple[ j ] = ++n;
            return i;
        }
    }
    return -1;
}

void main( int argc, char **argv ) {
    U32 n = argc > 1 ? atoi( argv[ 1 ] ) : 5;
    U32 m = argc > 2 ? atoi( argv[ 2 ] ) : n>>1;
    U32 i, t = 1;
    U8 *tuple = malloc( m );

    for( i = 0; i < m; ++i ) tuple[ i ] = i;

    for( i = 0; i < m; ++i ) printf( "%u ", tuple[ i ] ); printf( "\n"
+ );

    while( nextCombination( tuple, m-1, n-1 ) >= 0  ) {
        for( i = 0; i < m; ++i ) printf( "%u ", tuple[ i ] ); printf( 
+"\n" );
        ++t;
    }

    printf( "Iters:%I64u\n", t );
    free( tuple );
    return;
}
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Which works very nicely and very quickly.

I've updated the above to try and clarify.