JEE Mains · Maths · STD 11 - 6. permutation and combination
For \(\mathrm{n} \geq 2\), let \(S_n\) denote the set of all subsets of \(\{1,2 \ldots . . ., n\}\) with no two consecutive numbers. For example \(\{1,3,5\} \in \mathrm{S}_6\), but \(\{1,2,4\} \notin \mathrm{S}_6\). Then \(n\left(\mathrm{~S}_5\right)\) is equal to ________
- A 10
- B 11
- C 12
- D 13
Answer & Solution
Correct Answer
(D) 13
Step-by-step Solution
Detailed explanation
\(\mathrm{A}=\{1,2,3,4,5 \ldots . . . \mathrm{n}\}\) No. of subsets having \(r\) elements such that no two are consecutive is \(={ }^{n-r+1} C_r\) for \(\mathrm{n}=5\), no. of ways \(={ }^{6 \cdot \mathrm{r}} \mathrm{C}_{\mathrm{r}}\) Subsets having no element \(=1\) Subsets…
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