**Topic**

Given the set \(A = \left\{ {{x_1};{x_2};{x_3};…;{x_n}} \right\}\) has n elements. Calculate the number of subsets of A

**Solution method – See details**

The number of subsets of a set of n elements is \({2^n}\)

**Detailed explanation**

The number of subsets of a set of n elements is \({2^n}\)

Indeed,

+ The number of subsets with 0 elements of set A is: \(C_n^0\)

+ The number of subsets with 1 element of set A is: \(C_n^1\)

+ The number of subsets with 2 elements of set A is: \(C_n^2\)

…

+ The number of subsets with n elements of set A is: \(C_n^n\)

=> The number of subsets of the set of n elements is \(C_n^0 + C_n^1 + C_n^2 + … + C_n^n = {2^n}\)