How many subsets with more than two elements does a set with 100 elements have?

Solution:

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

A subset is a part of the set.

Given, a set contains 100 elements.

We have to find the total number of subsets.

A set with 'n' elements in it can have 2n subsets.

Here, n = 100

Subsets including the empty set are 2¹⁰⁰

Subsets excluding empty set = 2¹⁰⁰ - 1

Subset containing 1 element = 100

Subset containing 2 elements = (100 × 99)/2 = 4950

Now, possible subsets = 2¹⁰⁰ - 1 - 100 - 4950

= 2¹⁰⁰ - 5051

Therefore, the possible subsets are 2¹⁰⁰ - 5051.

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How many subsets with more than two elements does a set with 100 elements have?

Summary:

A set with 100 elements has 2¹⁰⁰ - 5051 subsets with more than two elements.