KCET · Maths · Binomial Theorem
If \(A=\{1,2,3,4,5,6\}\), then the number of subsets of A which contain at least two elements is
- A 64
- B 63
- C 57
- D 58
Answer & Solution
Correct Answer
(C) 57
Step-by-step Solution
Detailed explanation
Given set \(A=\{1,2,3,4,5,6\}\)
Number of subsets of \(A\) which contain at least two elements is \({ }^{6} C_{2}+{ }^{6} C_{3}+{ }^{6} C_{4}+{ }^{6} C_{5}+{ }^{6} C_{6}\)
\(=2^{6}-{ }^{6} C_{0}-{ }^{6} C_{1}=64-1-6=57\)
Number of subsets of \(A\) which contain at least two elements is \({ }^{6} C_{2}+{ }^{6} C_{3}+{ }^{6} C_{4}+{ }^{6} C_{5}+{ }^{6} C_{6}\)
\(=2^{6}-{ }^{6} C_{0}-{ }^{6} C_{1}=64-1-6=57\)
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