If A = {a, b, c, d}, how many subsets of A have at least three elements?
Answer and explanation
Correct answer: 5
The governing counting principle is that subsets with at least three elements have either exactly 3 elements or exactly 4 elements. From four distinct elements, the number of 3-element subsets is C(4,3) = 4, and the number of 4-element subsets is C(4,4) = 1. Hence the required total is 4 + 1 = 5. Option B is correct. Counting only triples gives 4, while including smaller subsets would overcount categories not requested.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing counting principle is that subsets with at least three elements have either exactly 3 elements or exactly 4 elements. From four distinct elements, the number of 3-element subsets is C(4,3) = 4, and the number of 4-element subsets is C(4,4) = 1. Hence the required total is 4 + 1 = 5. Option B is correct. Counting only triples gives 4, while including smaller subsets would overcount categories not requested.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
