If A = {1, 2, 3, 4}, how many three-element subsets are in P(A)?
Answer and explanation
Correct answer: 4
The power set P(A) contains every subset of A. A three-element subset is formed by choosing exactly 3 elements from the 4 elements of A. The number of such choices is C(4,3) = 4!/(3!1!) = 4. Therefore, P(A) contains exactly four subsets having three elements: {1,2,3}, {1,2,4}, {1,3,4}, and {2,3,4}. Hence option C is correct.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The power set P(A) contains every subset of A. A three-element subset is formed by choosing exactly 3 elements from the 4 elements of A. The number of such choices is C(4,3) = 4!/(3!1!) = 4. Therefore, P(A) contains exactly four subsets having three elements: {1,2,3}, {1,2,4}, {1,3,4}, and {2,3,4}. Hence option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
