If A = {a, b, c, d}, how many subsets of A have exactly two elements?
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Answer and explanation
Correct answer: 6
A subset with exactly two elements is formed by choosing any 2 of the 4 distinct elements a, b, c, and d. The order of selection does not matter, so we use combinations: C(4, 2) = 4!/(2!2!) = (4 × 3)/(2 × 1) = 6. Therefore, the six subsets are {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, and {c,d}.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A subset with exactly two elements is formed by choosing any 2 of the 4 distinct elements a, b, c, and d. The order of selection does not matter, so we use combinations: C(4, 2) = 4!/(2!2!) = (4 × 3)/(2 × 1) = 6. Therefore, the six subsets are {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, and {c,d}.
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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