Let $A$ be a set containing $n$ elements. A subset $P$ of the set $A$ is chosen at random. The set $A$ is reconstructed by replacing the elements of $P$, another subset $Q$ of set $A$ is chosen at random. What is the probability that $P\cap Q$ contains exactly $m$ elements, where $m<n$?
There are total $2^n$ subsets of a set having $n$ elements. But I don't have clear idea how to solve it. Please guide me.