How to Use the Subset & Power Set Calculator
How many subsets can you form from a set with n elements? Enter the element count and this calculator gives you the total number of subsets, along with the count of subsets containing exactly k elements if you'd like.
When building a subset, each element in the set has exactly two choices: it's either included or it isn't. With n elements, making this independent choice n times produces 2^n total possible outcomes. The set containing all of these subsets is called the power set, and it always includes both the empty set and the original set itself.
The number of subsets with exactly k elements is calculated with the combination formula nCk, also known as the binomial coefficient. For example, choosing 2 elements out of 5 gives 5C2 = 10 possibilities. This calculator processes the multiplication and division step by step as exact integers, so results stay accurate even as n grows — useful for combinatorics homework or double-checking probability calculations.
Frequently Asked Questions
When forming a subset, each element has exactly two choices: include it or leave it out. With n elements, making this independent choice n times gives 2 x 2 x ... x 2 (n times) = 2^n total possible subsets.
It's the binomial coefficient nCk, the number of ways to choose k elements out of n without regard to order. This calculator computes it step by step as an integer, so it stays exact even for large values of n.