If A = {p, q, r, s}, how many 2-element subsets of A are there?
Answer and explanation
Correct answer: 6
A 2-element subset is formed by choosing 2 different elements from the 4-element set A. Since the order of elements does not matter in a set, combinations are used rather than permutations. The number is C(4, 2) = 4!/(2!2!) = (4 × 3)/2 = 6. The six subsets are {p,q}, {p,r}, {p,s}, {q,r}, {q,s}, and {r,s}. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
A 2-element subset is formed by choosing 2 different elements from the 4-element set A. Since the order of elements does not matter in a set, combinations are used rather than permutations. The number is C(4, 2) = 4!/(2!2!) = (4 × 3)/2 = 6. The six subsets are {p,q}, {p,r}, {p,s}, {q,r}, {q,s}, and {r,s}. Therefore, option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
