Showcase of math equations

Let $f=x^2+\frac{1}{11}$:

$$\begin{array}{rl}& \mathbb{P}(X+Y=k)=\sum _{x\in X(\Omega )}\mathbb{P}(X=x)\cdot \mathbb{P}(Y=k-x)\\ & =\sum _{x=0}^n\left(\genfrac{}{}{0ex}{}{n}{x}\right)p^x(1-p{)}^{n-x}\cdot (\genfrac{}{}{0ex}{}{m}{k-x})q^{k-x}(1-q{)}^{m-(k-x)}\end{array}$$

\documentclass{article}
\usepackage{mathtools,amssymb,amsfonts}
\begin{document}
Let $f = x^2 + \frac{1}{11}$:
\begin{align*} \qquad&\hspace{-2em}
\mathbb{P}(X+Y=k) 
= \sum_{\mathclap{x \in X(\Omega)}} \mathbb{P}(X = x) \cdot \mathbb{P}(Y=k-x) \\&
= \sum_{x = 0}^n \binom{n}{x}\, p^x\, (1-p)^{n-x} \cdot \binom{m}{k-x}\, q^{k-x}\, (1-q)^{m-(k-x)}
\end{align*}
\end{document}