Math

Subset Calculator

Count how many subsets and k-element subsets a set has.

Calculated Output

All subsets (2ⁿ) 32

k-element subsets 10

Formula: k-subsets = C(n, k) = n! ÷ (k!(n−k)!)

Step-by-Step Breakdown

1. Values used:

2. Set size n = 5

3. Subset size k = 2

5. All subsets (2ⁿ) = 32

6. k-element subsets = Set size n x Subset size k = 5 x 2 = 10

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The math behind it

A set of n elements has 2ⁿ subsets in total. The number with exactly k elements is the binomial coefficient C(n, k).

A 5-element set has 32 subsets; 10 of them have exactly 2 elements.

What is a proper subset?

A subset that is not equal to the original set — there are 2ⁿ − 1 of them.