If A = {1, 2, 3, 4, 5, 6}, among the 3-element subsets in P(A), how many contain 1?
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Answer and explanation
Correct answer: 10
The element 1 must be included in every required subset, so it is fixed. We only need to choose the remaining 2 elements from the other 5 elements, namely {2, 3, 4, 5, 6}. The number of choices is C(5,2) = 5 × 4 / 2 = 10. Thus, exactly 10 three-element subsets contain 1, making option B correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The element 1 must be included in every required subset, so it is fixed. We only need to choose the remaining 2 elements from the other 5 elements, namely {2, 3, 4, 5, 6}. The number of choices is C(5,2) = 5 × 4 / 2 = 10. Thus, exactly 10 three-element subsets contain 1, making option B 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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