1. Problem: How many subsets does a set with $n$ elements have? 2. Formula: The number of subsets of a set with $n$ elements is given by $$2^n$$ because each element can either be in or out of a subset. 3. Explanation: For each element, there are 2 choices (include or exclude), so total subsets = $2 \times 2 \times \cdots \times 2 = 2^n$. 4. Final answer: The number of subsets of a set with $n$ elements is $$2^n$$.