$A$ is a set containing $n$ different elements. A subset $P$ of $A$ is chosen. The set $A$ is reconstructed by replacing the elements of $P$. A subset $Q$ of $A$ is again chosen. The number of ways of choosing $P$ and $Q$ so that $P\cap Q$ contains exactly two elements is a. ${.}^n{C}_3\times 2^n$ b. ${.}^n{C}_2\times 3^{n-2}$ c. $3^{n-1}$ d. none of these

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