If A = {1, 2, 3, 4, 5}, how many subsets of A have three or more elements?
Answer and explanation
Correct answer: 16
A subset with three or more elements can have exactly 3, 4, or 5 elements. Using combinations, the counts are C(5,3) = 10, C(5,4) = 5, and C(5,5) = 1. Therefore the total is 10 + 5 + 1 = 16, so option B is correct. The value 10 counts only triples, 20 does not correspond to this sum, and 26 includes an incorrect extra category.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
A subset with three or more elements can have exactly 3, 4, or 5 elements. Using combinations, the counts are C(5,3) = 10, C(5,4) = 5, and C(5,5) = 1. Therefore the total is 10 + 5 + 1 = 16, so option B is correct. The value 10 counts only triples, 20 does not correspond to this sum, and 26 includes an incorrect extra category.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
