For a given set of n elements: The number of subsets with no elements =nC0=C0 The number of subsets with 1 element = The number of ways in which 1 element can be selected from n elements =nC1=C1. The number of subsets with 2 elements = The number of ways in which 2 elements can be selected from n elements =−C2=C2. And so on. ∴ The total number of subsets =C0+C1+C2+C3+.........+Cn−1+Cn=2n