If A = {a, b, c, d, e, f}, how many subsets with exactly 5 elements are in P(A)?
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Answer and explanation
Correct answer: 6
A five-element subset is obtained by selecting 5 of the 6 elements of A. The number of selections is C(6,5) = 6!/(5!1!) = 6. Equivalently, each such subset is formed by omitting exactly one element from A, and there are six possible elements to omit. Hence P(A) contains exactly six subsets with five elements.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A five-element subset is obtained by selecting 5 of the 6 elements of A. The number of selections is C(6,5) = 6!/(5!1!) = 6. Equivalently, each such subset is formed by omitting exactly one element from A, and there are six possible elements to omit. Hence P(A) contains exactly six subsets with five elements.
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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