If A = {1, 2, 3, 4, 5}, how many subsets have at least 4 elements?
Answer and explanation
Correct answer: 6
A subset with at least 4 elements can have either exactly 4 elements or exactly 5 elements. The number of 4-element subsets is C(5,4) = 5, and the number of 5-element subsets is C(5,5) = 1. Therefore, the required number is 5 + 1 = 6. Hence option B is correct. The answer 5 counts only the four-element subsets and misses the whole set.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A subset with at least 4 elements can have either exactly 4 elements or exactly 5 elements. The number of 4-element subsets is C(5,4) = 5, and the number of 5-element subsets is C(5,5) = 1. Therefore, the required number is 5 + 1 = 6. Hence option B is correct. The answer 5 counts only the four-element subsets and misses the whole set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
