If A has n elements and P(A) has 64 elements, how many 3-element subsets does A have?
Answer and explanation
Correct answer: 20
A set with n elements has exactly 2^n subsets, so |P(A)| = 2^n = 64 = 2^6. Hence n = 6. The number of 3-element subsets of a six-element set is the combination C(6, 3) = 6!/(3!3!) = (6 × 5 × 4)/(3 × 2 × 1) = 20. Therefore, option C is correct. The value 15 would count 2-element subsets, not 3-element subsets, which is a common error.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
A set with n elements has exactly 2^n subsets, so |P(A)| = 2^n = 64 = 2^6. Hence n = 6. The number of 3-element subsets of a six-element set is the combination C(6, 3) = 6!/(3!3!) = (6 × 5 × 4)/(3 × 2 × 1) = 20. Therefore, option C is correct. The value 15 would count 2-element subsets, not 3-element subsets, which is a common error.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
