If A = {1, 2, 3, 4, 5}, how many subsets in P(A) have exactly 2 or exactly 3 elements?
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Answer and explanation
Correct answer: 20
The number of two-element subsets of a five-element set is C(5,2) = 10. The number of three-element subsets is C(5,3) = 10. These two classes are disjoint because a subset cannot simultaneously have two and three elements. Therefore, the required total is 10 + 10 = 20.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The number of two-element subsets of a five-element set is C(5,2) = 10. The number of three-element subsets is C(5,3) = 10. These two classes are disjoint because a subset cannot simultaneously have two and three elements. Therefore, the required total is 10 + 10 = 20.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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