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Combinations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSCombinations3 Marks
Question
If ${^\text{15}}\text{C}_{\text{r}}:{^\text{15}}\text{C}_{\text{r-1}},=11:5,$ Find r.
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Answer

We have,
$\frac{{^\text{15}}\text{C}_{\text{r}}}{{^\text{15}}\text{C}_{\text{r}-1}}=\frac{11}{5}$
$\Rightarrow \frac{15-\text{r}+1}{\text{r}}=\frac{11}{5}$
$\Rightarrow 75-5\text{r}+5=11\text{r}$
$\Rightarrow\ 16\text{r}=80$
$\Rightarrow \text{r}=5$

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