If A = {1, 2, 3, 4, 5}, how many elements of P(A) have exactly 3 elements?
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Answer and explanation
Correct answer: 10
An element of P(A) is a subset of A. To form a subset containing exactly three elements from the five elements of A, choose any 3 of them. The number of such choices is the combination 5C3 = 5!/(3!2!) = (5 × 4)/(2 × 1) = 10. Therefore, exactly 10 elements of P(A) have cardinality 3, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
An element of P(A) is a subset of A. To form a subset containing exactly three elements from the five elements of A, choose any 3 of them. The number of such choices is the combination 5C3 = 5!/(3!2!) = (5 × 4)/(2 × 1) = 10. Therefore, exactly 10 elements of P(A) have cardinality 3, so 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.
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