title: Iterating over all subsets of a given size
body: <p>I know that iterating over all subsets of a set of size n is a performance nightmare and will take O(2^n) time.</p>
  
  <p>How about iterating over all subsets of size k (for (0 &lt;= k &lt;= n))?  Is that a performance nightmare?  I know there are (n, k) = n! / k! (n - k)! possibilities.  I know that if k is very close to 0 or very close to n, this is a small number.</p>
  
  <p>What is the worst case performance in terms of n and k?  Is there a simpler way of saying it other than just O(n! / k! (n - k)!)?  Is this asymptotically smaller than O(n!) or the same?</p>