If A = {1, 2, 3, 4, 5, 6, 7}, how many subsets in P(A) have at least 5 elements?
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Answer and explanation
Correct answer: 29
At least 5 elements means that the subset may contain 5, 6, or 7 elements. The numbers of such subsets are C(7,5) = 21, C(7,6) = 7, and C(7,7) = 1. Therefore, the total is 21 + 7 + 1 = 29. The phrase 'at least' requires inclusion of every size greater than or equal to 5, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
At least 5 elements means that the subset may contain 5, 6, or 7 elements. The numbers of such subsets are C(7,5) = 21, C(7,6) = 7, and C(7,7) = 1. Therefore, the total is 21 + 7 + 1 = 29. The phrase 'at least' requires inclusion of every size greater than or equal to 5, so 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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