Solution :
Let A be a finite set containing n elements. Let 0 \(\le\) r \(\le\) n.
Consider those subsets of A that have r elements each. We know that the number of ways in which r elements can be chosen out of n elements is \(^nC_r\).
Therefore, the number of subsets of A having r elements each is \(^nC_r\).
Hence, the total number of subsets of A
= \(^nC_0\) + \(^nC_1\) + \(^nC_2\) + …. + \(^nC_n\) = \((1 + 1)^n\) = \(2^n\).
[ Using binomial theorem ]