If A = {1, 2, 3, 4, 5}, how many subsets of A contain exactly two elements?
Answer and explanation
Correct answer: 10
An exactly two-element subset is formed by choosing two different elements from the five elements of A. Since the order of selection does not matter, combinations are used: C(5, 2) = 5!/(2!3!) = (5 × 4)/2 = 10. Thus there are 10 such subsets. The value 20 would count ordered selections using permutations, while 5 and 25 do not represent the number of two-element subsets. Every pair is counted once, regardless of its order.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
An exactly two-element subset is formed by choosing two different elements from the five elements of A. Since the order of selection does not matter, combinations are used: C(5, 2) = 5!/(2!3!) = (5 × 4)/2 = 10. Thus there are 10 such subsets. The value 20 would count ordered selections using permutations, while 5 and 25 do not represent the number of two-element subsets. Every pair is counted once, regardless of its order.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
