If A = {0, 1, 2, 3}, how many two-element subsets contain 0?
Answer and explanation
Correct answer: 3
The subset must contain 0, so one of its two positions is already fixed. The second element can be chosen from the remaining elements of A: 1, 2, or 3. These choices produce the three distinct subsets {0, 1}, {0, 2}, and {0, 3}. No other two-element subset containing 0 is possible. Equivalently, we choose one element from the three available elements, giving C(3, 1) = 3. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The subset must contain 0, so one of its two positions is already fixed. The second element can be chosen from the remaining elements of A: 1, 2, or 3. These choices produce the three distinct subsets {0, 1}, {0, 2}, and {0, 3}. No other two-element subset containing 0 is possible. Equivalently, we choose one element from the three available elements, giving C(3, 1) = 3. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
