If |A| = 6, how many members of the power set P(A) have exactly 4 elements?
Answer and explanation
Correct answer: 15
The power set P(A) consists of all subsets of A. A member of P(A) having exactly 4 elements is therefore a 4-element subset of A. Since A has 6 elements, the number of such subsets is C(6, 4) = 6!/(4!2!) = (6 × 5)/(2 × 1) = 15. Equivalently, choosing 4 elements to include is the same as choosing the 2 elements to exclude, so C(6, 4) = C(6, 2) = 15. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The power set P(A) consists of all subsets of A. A member of P(A) having exactly 4 elements is therefore a 4-element subset of A. Since A has 6 elements, the number of such subsets is C(6, 4) = 6!/(4!2!) = (6 × 5)/(2 × 1) = 15. Equivalently, choosing 4 elements to include is the same as choosing the 2 elements to exclude, so C(6, 4) = C(6, 2) = 15. Hence 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.
