Is this problem hard? Finding all the subsets of size k from a sequence of n numbers I want to know the hardness of finding all subsets of size k from a sequence of n numbers. There is an algorithm based on recursion: Print all possible combinations of r elements in a given array of size n.

However, I am not sure whether this can be done in polynomial time or not.
For fixed $k$, the running time is polynomial, but if $k$ is part of the input, the running time is not polynomial. The number of such subsets is ${n \choose k}$, which is very roughly like $n^k$.  Thus, if $k$ is fixed to something like 3, this becomes $O(n^3)$ -- polynomial.  However, if $k$ is part of the input, the running time is exponential in $k$.