If A = {1, 2, 3, 4, 5}, how many sets in P(A) have exactly 3 elements?
Answer and explanation
Correct answer: 10
A subset with exactly three elements is formed by choosing three elements from the five elements of A. The number of such choices is the combination C(5,3) = 5!/(3!2!) = 10. Each distinct choice gives one distinct subset, and every subset of A is an element of P(A). Hence, P(A) contains 10 subsets having exactly three elements.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
A subset with exactly three elements is formed by choosing three elements from the five elements of A. The number of such choices is the combination C(5,3) = 5!/(3!2!) = 10. Each distinct choice gives one distinct subset, and every subset of A is an element of P(A). Hence, P(A) contains 10 subsets having exactly three elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
