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If ${ }^{2 n} C_3:{ }^n C_2=44: 3$, then for which of the following values of $r$, the value of ${ }^n C_r$ will be 15
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The correct answer is:
$r=5$
${ }^{15} C_{3 r}={ }^{15} C_{r+3} \Rightarrow{ }^{15} C_{15-3 r}={ }^{15} C_{r+3}$
$\Rightarrow 15-3 r=r+3 \Rightarrow r=3$.
$\Rightarrow 15-3 r=r+3 \Rightarrow r=3$.
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