If A = {1, 2, 3, 4, 5}, how many four-element subsets are in P(A)?
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Answer and explanation
Correct answer: 5
A four-element subset is obtained by choosing 4 of the 5 elements of A. The number of choices is 5C4 = 5!/(4!1!) = 5. Equivalently, each four-element subset is determined by the one element left out, and there are five possible elements to omit. Therefore, P(A) has exactly five subsets containing four elements.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
A four-element subset is obtained by choosing 4 of the 5 elements of A. The number of choices is 5C4 = 5!/(4!1!) = 5. Equivalently, each four-element subset is determined by the one element left out, and there are five possible elements to omit. Therefore, P(A) has exactly five subsets containing four 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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