यदि \(A=\{1,2,3,4,5,6\}\), तो (\mathcal{P}(A)) के कितने तत्वों में (1,2,3) में से कम से कम दो तत्व होंगे?
If \(A=\{1,2,3,4,5,6\}\), how many elements of (\mathcal{P}(A)) contain at least two elements from (1,2,3)?
Explanation opens after your attempt
Correct Answer
C. (32)
Concept
Choosing at least two from (1,2,3) gives \(\binom{3}{2}+\binom{3}{3}=4\) ways. The remaining three elements are free, so the count is \(4\times2^3=32\).
Why this answer is correct
The correct answer is C. (32). Choosing at least two from (1,2,3) gives \(\binom{3}{2}+\binom{3}{3}=4\) ways. The remaining three elements are free, so the count is \(4\times2^3=32\).
Exam Tip
(1,2,3) में से कम से कम दो चुनने के \(\binom{3}{2}+\binom{3}{3}=4\) तरीके हैं। शेष तीन तत्व स्वतंत्र हैं, इसलिए \(4\times2^3=32\) है।
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