C で n 個の項目の k 個の組み合わせをすべて生成するにはどうすればよいですか?

#include <iostream>
#include <vector>
using namespace std;

void combinations(vector<int>& items, int k) {
  int n = items.size();

  for (int bitmask = 0; bitmask < (1 << n); bitmask++) {
    vector<int> combination;
    for (int i = 0; i < n; i++) {
      if ((bitmask >> i) & 1) {
        combination.push_back(items[i]);
      }
    }
    cout << "Combination: ";
    for (int item : combination) {
      cout << item << " ";
    }
    cout << endl;
  }
}

int main() {
  vector<int> items = {1, 2, 3, 4, 5};
  int k = 3;
  combinations(items, k);
  return 0;
}

Combination: 1 2 3
Combination: 1 2 4
Combination: 1 2 5
Combination: 1 3 4
Combination: 1 3 5
Combination: 1 4 5
Combination: 2 3 4
Combination: 2 3 5
Combination: 2 4 5
Combination: 3 4 5