JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(\mathrm{S}=\{1,2,3,4,5,6,9\} .\) Then the number of elements in the set \(\mathrm{T}=\{\mathrm{A} \subseteq \mathrm{S}: \mathrm{A} \neq \phi\) and the sum of all the elements of \(\mathrm{A}\) is not a multiple of 3\(\}\) is ..... .
- A \(20\)
- B \(40\)
- C \(80\)
- D \(120\)
Answer & Solution
Correct Answer
(C) \(80\)
Step-by-step Solution
Detailed explanation
\(3n\) type \(\quad \rightarrow 3,6,9=\mathrm{P}\) \(3 \mathrm{n}-1 \quad\) type \(\rightarrow 2,5=\mathrm{Q}\) \(3 \mathrm{n}-2\quad\) type \(\rightarrow 1,4=\mathrm{R}\) number of subset of \(S\) containing one element which are not divisible by \(3\)…
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