Let A = {a, b, c, d, e, f}. How many elements of the power set P(A) have exactly three elements and do not contain a?
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Answer and explanation
Correct answer: 10
An element of P(A) is a subset of A. Since the required subset must not contain a, a is excluded, leaving the five elements {b, c, d, e, f}. We must choose exactly three elements from these five, so the number of valid subsets is C(5,3) = 5!/(3!2!) = 10. Therefore, option A 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. Since the required subset must not contain a, a is excluded, leaving the five elements {b, c, d, e, f}. We must choose exactly three elements from these five, so the number of valid subsets is C(5,3) = 5!/(3!2!) = 10. Therefore, option A 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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