If A = {1, 2, 3, 4, 5, 6}, how many elements of P(A) contain at least two elements from {1, 2, 3}?
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Answer and explanation
Correct answer: 32
An element of P(A) is a subset of A. Among the three specified elements 1, 2, and 3, at least two can be selected in C(3,2) + C(3,3) = 3 + 1 = 4 ways. Each of the remaining elements 4, 5, and 6 may independently be selected or omitted, giving 2^3 = 8 choices. Hence the total is 4 × 8 = 32, so option C is correct.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
An element of P(A) is a subset of A. Among the three specified elements 1, 2, and 3, at least two can be selected in C(3,2) + C(3,3) = 3 + 1 = 4 ways. Each of the remaining elements 4, 5, and 6 may independently be selected or omitted, giving 2^3 = 8 choices. Hence the total is 4 × 8 = 32, so option C is correct.
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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