How many subsets are there that contain a specific set? Given a set $S=\{1, 2, 3, ..., n\}$, how do I find all subsets of size $k$ that contain the set $\{1, 2\}$?
I know that $\binom{n}{k}$ would give me all subsets of size $k$, but I can't seem to find a way to find just the ones that have that subset. 

Hint: If you know that it must contain $\{1,2\}$, then you have to choose elements from $\{3,4,\ldots,n\}$.  So choosing a subset of $\{1,2,\ldots,n\}$ that contains $\{1,2\}$ is the same as choosing what?
