If |A| = 7, how many elements of the power set P(A) have at least 6 elements?
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Answer and explanation
Correct answer: 8
A subset having at least six elements can have exactly six elements or exactly seven elements, because A itself has only seven elements. The number of six-element subsets is C(7,6) = 7, and the number of seven-element subsets is C(7,7) = 1. Therefore, the required total is 7 + 1 = 8, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A subset having at least six elements can have exactly six elements or exactly seven elements, because A itself has only seven elements. The number of six-element subsets is C(7,6) = 7, and the number of seven-element subsets is C(7,7) = 1. Therefore, the required total is 7 + 1 = 8, 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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