If A = {1, 2, 3, 4, 5}, how many subsets have exactly 2 elements and do not contain 5?
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Answer and explanation
Correct answer: 6
Because 5 must not be included, remove it from consideration. We must choose exactly two elements from the remaining four-element set {1, 2, 3, 4}. The number of choices is the combination 4C2 = 4!/(2!2!) = 6. These pairs are {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}; therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
Because 5 must not be included, remove it from consideration. We must choose exactly two elements from the remaining four-element set {1, 2, 3, 4}. The number of choices is the combination 4C2 = 4!/(2!2!) = 6. These pairs are {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}; 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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