NIMCET 2016 Question Paper with solutions

Given, S = {1,2 ..... n}
First chose a k element subset B of S.This can be done in $\left(\begin{array}{c}\mathit{n}\\ \mathit{k}\end{array}\right)$ ways
Given the subset B,A has $2^{\mathit{k}}-1$ options(since the numbers of proper subset of a k- element let is $2^{\mathit{k}}-1$)
Hence, the total number of pairs of sets (A B) such that A ⊆ B is given by

$=3^{\mathit{n}}-2^{\mathit{n}}$
None option is correct.