A subset contains some (or none, or all) of the elements of a set. Counting subsets answers questions like “how many pizza topping combinations are there?” – with 8 toppings, 256, including the plain pizza.
How to use the Subset Calculator
- Enter
- Set elements (separate with commas)
- Number of elements n
- Subset size k
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter the elements, or just the number of elements for large sets. Proper subsets exclude the set itself; the number of subsets of size k is the binomial coefficient.
Formula
Subsets = 2ⁿ, proper subsets = 2ⁿ − 1, k-element subsets = C(n, k)
Worked example
Inputs — Enter: Set elements; Set elements (separate with commas): 1, 2, 3, 4; Subset size k: 2.
Results — Number of subsets = 16; Number of proper subsets = 15; Subsets with k elements = 6; All subsets = ∅, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {2, 3}, {1, 4}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}.
Key terms
- Subset
- A set whose elements all belong to another set.
Frequently asked questions
What is a proper subset?
A subset that is not equal to the original set.
How many subsets does {1, 2, 3} have?
8: ∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.
Is every set a subset of itself?
Yes, but not a proper subset.
How many 2-element subsets does a 10-element set have?
C(10, 2) = 45.