If \(A=\{2,3,4,5,6\}\), how many four-element subsets are in \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: 5
The set \(A\) has five elements, and a four-element subset is formed by choosing four of those five elements. The number of choices is \(\binom{5}{4}=\frac{5!}{4!1!}=5\). Equivalently, each four-element subset is obtained by leaving out exactly one of the five elements. Thus \(\mathcal{P}(A)\) contains exactly five subsets having four elements, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The set \(A\) has five elements, and a four-element subset is formed by choosing four of those five elements. The number of choices is \(\binom{5}{4}=\frac{5!}{4!1!}=5\). Equivalently, each four-element subset is obtained by leaving out exactly one of the five elements. Thus \(\mathcal{P}(A)\) contains exactly five subsets having four elements, 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.
