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JEE Mains · Maths · STD 11 - 6. permutation and combination
If \({ }^{1} \mathrm{P}_{1}+2 \cdot{ }^{2} \mathrm{P}_{2}+3 \cdot{ }^{3} \mathrm{P}_{3}+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}={ }^{\mathrm{q}} \mathrm{P}_{\mathrm{r}}-\mathrm{s}, 0 \leq \mathrm{s} \leq 1\) then \({ }^{\mathrm{q}+\mathrm{s}} \mathrm{C}_{\mathrm{r}-\mathrm{s}}\) is equal to .... .
- A \(136\)
- B \(1\)
- C \(16\)
- D \(13\)
Answer & Solution
Correct Answer
(A) \(136\)
Step-by-step Solution
Detailed explanation
\({ }^{1} \mathrm{P}_{1}+2 \cdot{ }^{2} \mathrm{P}_{2}+3 \cdot{ }^{3} \mathrm{P}_{3}+\ldots+15 \cdot{ }^{15} \mathrm{P}_{15}\) \(=1 !+2.2 !+3.3 !+\ldots .15 \times 15 !\) \(=\sum_{\mathrm{r}=1}^{15}(\mathrm{r}+1-1) \mathrm{r} !\)…
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