How many subsets does a set with 5 elements have in total?
Answer and explanation
Correct answer: 32
For each element of a set, a subset has two independent choices: the element is either included or excluded. Thus, a set with n elements has 2ⁿ subsets in total. For n = 5, the number is 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. This count includes both the empty set and the original set itself. Therefore, option C, 32, is correct; 25 and 120 come from unrelated calculations such as 5² and 5!.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
For each element of a set, a subset has two independent choices: the element is either included or excluded. Thus, a set with n elements has 2ⁿ subsets in total. For n = 5, the number is 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. This count includes both the empty set and the original set itself. Therefore, option C, 32, is correct; 25 and 120 come from unrelated calculations such as 5² and 5!.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
