If A = {1, 2, 3, 4, 5, 6}, how many subsets in P(A) have exactly 4 elements?
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Answer and explanation
Correct answer: 15
We must choose exactly 4 elements from the 6 elements of A. The order of selection does not matter, so combinations are used. The required number is C(6,4) = 6!/(4!2!) = (6 × 5)/(2 × 1) = 15. Every four-element subset of A belongs to P(A), so there are 15 such subsets and option B is correct.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
We must choose exactly 4 elements from the 6 elements of A. The order of selection does not matter, so combinations are used. The required number is C(6,4) = 6!/(4!2!) = (6 × 5)/(2 × 1) = 15. Every four-element subset of A belongs to P(A), so there are 15 such subsets and 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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