Algorithm by Donald Knuth

comb_amount.c

unsigned long long
choose(unsigned long long n, unsigned long long k) {
        if (k > n) {
                return 0;
        }
        unsigned long long r = 1;
        for (unsigned long long d = 1; d <= k; ++d) {
                r *= n--;
                r /= d;
        }
        return r;
}

combinations.c

/* Algorithm by Donald Knuth. */
#include <stdio.h>
#include <stdlib.h>

void main( void)
{
	int i, j=1, k, n, *c, x;
	printf( "Enter n,k: ");
	scanf( "%d,%d", &n, &k);
	c = malloc( (k+3) * sizeof(int));

	for (i=1; i <= k; i++) c[i] = i;
	c[k+1] = n+1;
	c[k+2] = 0;
	j = k;

visit:
	for (i=k; i >= 1; i--) printf( "%3d", c[i]);
	printf( "\n");
	if (j > 0) {x = j+1; goto incr;}
	if (c[1] + 1 < c[2])
	 {
	 c[1] += 1;
	 goto visit;
	 }
	j = 2;

do_more:
	c[j-1] = j-1;
	x = c[j] + 1;
	if (x == c[j+1]) {j++; goto do_more;}
	if (j > k) exit(0);

incr:
	c[j] = x;
	j--;
	goto visit;
}