If A = {1, 2, 3, 4}, how many subsets of A have exactly 3 elements?
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Answer and explanation
Correct answer: 4
A subset with exactly 3 elements is formed by choosing 3 elements from the 4 elements of A. The number of such choices is C(4,3) = 4. They are {1,2,3}, {1,2,4}, {1,3,4}, and {2,3,4}. The order of elements does not matter in a set, so arrangements are not counted separately. Therefore, option B is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
A subset with exactly 3 elements is formed by choosing 3 elements from the 4 elements of A. The number of such choices is C(4,3) = 4. They are {1,2,3}, {1,2,4}, {1,3,4}, and {2,3,4}. The order of elements does not matter in a set, so arrangements are not counted separately. Therefore, option B is correct.
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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