Let $\pi$ be a random permutation of $n$ objects and let $ T := \text{the number of transpositions in } \pi $. Use Chebychev's Inequality to find an upper bound for $T\geqslant k$.
Okay the problem I'm having here is with $\mathbb{Var}(T)$, I'm not sure how to find it. I know the expectation is $\frac{1}{2}$, so my formula so far is $$\mathbb{P}\left(T-\frac{1}{2}\geqslant k\right) \leqslant \frac{\mathbb{Var}(T)}{k^2}$$