If A has 4 elements, what is the number of 2-element subsets of P(A)?
Answer and explanation
Correct answer: 120
If A has 4 elements, then its power set P(A) has 2⁴ = 16 elements. The question does not ask for the number of 2-element subsets of A; it asks for the number of 2-element subsets of P(A), which is a new set containing 16 elements. Therefore, we choose 2 elements from 16: C(16, 2) = 16 × 15 ÷ 2 = 120. Hence option C is correct. The key idea is to calculate the size of the power set first and then use combinations.
Frequently asked questions
What is the correct answer to this question?
120
Why is this the correct answer?
If A has 4 elements, then its power set P(A) has 2⁴ = 16 elements. The question does not ask for the number of 2-element subsets of A; it asks for the number of 2-element subsets of P(A), which is a new set containing 16 elements. Therefore, we choose 2 elements from 16: C(16, 2) = 16 × 15 ÷ 2 = 120. Hence option C is correct. The key idea is to calculate the size of the power set first and then use combinations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
