If A = {1, 2, 3, 4, 5, 6}, how many three-element subsets of A must contain 1?
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Answer and explanation
Correct answer: 10
Because the element 1 must be included, it is already fixed as one member of every required subset. We therefore need to choose the remaining 2 elements from the other 5 elements, namely 2, 3, 4, 5, and 6. The number of choices is C(5, 2) = 5!/(2!3!) = 10. Hence, exactly 10 three-element subsets contain 1.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
Because the element 1 must be included, it is already fixed as one member of every required subset. We therefore need to choose the remaining 2 elements from the other 5 elements, namely 2, 3, 4, 5, and 6. The number of choices is C(5, 2) = 5!/(2!3!) = 10. Hence, exactly 10 three-element subsets contain 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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