We find the Hilbert function and the minimal free resolution of a star-configuration in $mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $mathbb{P}^2$ is generic or non-generic We also prove that if $mathbb{X}$ and $mathbb{Y}$ are linear star-configurations in $mathbb{P}^2$ of types t and s, respectively, with $s{geq}t{geq}3$, then the Artinian k-algebra $R/(I_{mathbb{X}}+I_{mathbb{Y})$ has the weak Lefschetz property.