If A = {p, q, r, s}, how many subsets of A have exactly two elements?
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Answer and explanation
Correct answer: 6
A two-element subset is formed by choosing 2 elements from the 4 elements of A, and order does not matter. Hence the number is C(4,2) = 4!/(2!2!) = 6. For example, {p,q} and {q,p} are the same subset, so permutations must not be counted separately. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A two-element subset is formed by choosing 2 elements from the 4 elements of A, and order does not matter. Hence the number is C(4,2) = 4!/(2!2!) = 6. For example, {p,q} and {q,p} are the same subset, so permutations must not be counted separately. Therefore 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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