Is this problem hard? Finding all the subsets of size k from a sequence of n numbers
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 $k$.