Let A = {1, 2, 3, 4, 5, 6}. Among the 3-element subsets in the power set P(A), how many do not contain the element 1?
Answer and explanation
Correct answer: 10
A 3-element subset that does not contain 1 must be formed entirely from the remaining five elements, {2, 3, 4, 5, 6}. Thus, the problem is equivalent to choosing 3 elements from these 5 elements. The number of choices is C(5,3) = 5!/(3!2!) = (5 × 4 × 3)/(3 × 2 × 1) = 10. Hence, exactly 10 three-element subsets of A exclude the element 1.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
A 3-element subset that does not contain 1 must be formed entirely from the remaining five elements, {2, 3, 4, 5, 6}. Thus, the problem is equivalent to choosing 3 elements from these 5 elements. The number of choices is C(5,3) = 5!/(3!2!) = (5 × 4 × 3)/(3 × 2 × 1) = 10. Hence, exactly 10 three-element subsets of A exclude the element 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
