if $^{15} C_{r} :^{15} C_{r} = 11 : 5$ find $r$

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Solution

$_{r}^{15} C :_{r - 1}^{15} C = 11 : 5 \Rightarrow \frac{\frac{15!}{(15 - r)! r!}}{\frac{15!}{(15 - r + 1)! (r - 1)!}} = \frac{11}{5} \Rightarrow \frac{15 - r + 1}{r} = \frac{11}{5} \Rightarrow r = 5$

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