What is the probability of getting any s of a kind (let's say 3 of a kind) when dealt n cards (let's say 13) of a standar deck? I have calculated the probability of getting a specific set of 3 of a kind (i.e. 3 Kings) which is $ \frac{\left( \begin{array}{c} 4\\ 3 \end{array} \right) \left( \begin{array}{c} 52-3\\ 13-3 \end{array} \right)}{\left( \begin{array}{c} 52\\ 13 \end{array} \right)} $ (please correct me if I'm wrong).
However, what I am trying to find is the probability of getting any s of a kind, and furthermore the probability of getting any s of a kind greater than one specific value.