If A = {1, 2, 3, 4, 5}, how many three-element subsets are there in P(A)?
Answer and explanation
Correct answer: 10
To form a three-element subset from the five elements of A, choose any 3 elements without considering their order. Therefore, the required number is C(5,3) = 5!/(3!2!) = (5×4×3)/(3×2×1) = 10. These are ten distinct members of P(A). The total number of all subsets is 2^5 = 32, but only the subsets with exactly three elements are counted here.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
To form a three-element subset from the five elements of A, choose any 3 elements without considering their order. Therefore, the required number is C(5,3) = 5!/(3!2!) = (5×4×3)/(3×2×1) = 10. These are ten distinct members of P(A). The total number of all subsets is 2^5 = 32, but only the subsets with exactly three elements are counted here.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
