If A = {1, 2, 3, 4, 5}, how many two-element subsets of A do not contain 5?
Answer and explanation
Correct answer: 6
A two-element subset that does not contain 5 must be formed entirely from the remaining set {1, 2, 3, 4}. We therefore choose any two of these four elements. The number of choices is C(4,2) = 4×3/2 = 6. The value 10 would count all two-element subsets of A and would incorrectly include the four subsets containing 5.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A two-element subset that does not contain 5 must be formed entirely from the remaining set {1, 2, 3, 4}. We therefore choose any two of these four elements. The number of choices is C(4,2) = 4×3/2 = 6. The value 10 would count all two-element subsets of A and would incorrectly include the four subsets containing 5.
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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