How many subsets of a set with 100 elements have more than one element?

Solution:

A set is a well-defined collection of numbers, alphabets, objects, or any items.

A subset is a part of the set.

A set is a collection of different objects.

Set A is a subset of set B if all the elements in set A are present in set B.

Here, A is called the subset, and B is called the superset. 

Number of subsets having more than 1 element

= {Total number of subsets possible} - {Number of subsets possible with no elements} - {Number of subsets possible with one element}

= 2¹⁰⁰ - (¹⁰⁰C₁ + 1)

= 2¹⁰⁰ - (100 + 1)

= 2¹⁰⁰ - 101

How many subsets of a set with 100 elements have more than one element?

Summary:

(2¹⁰⁰ - 101) subsets of a set with 100 elements have more than one element.