If ^15 C_ 3r = ^15 C_ r+3 , Find r. - Vidyadip

Question

If ${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$ Find $r$.

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Answer

We have, If ${ }^{\mathrm{n}} \mathrm{C}_{\mathrm{p}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{q}}=\mathrm{n}$
Then $\mathrm{p}+\mathrm{q}=\mathrm{n}$
Also, ${ }^{15} \mathrm{C}_{3 \mathrm{r}}={ }^{15} \mathrm{C}_{\mathrm{r}+3}, $
$\Rightarrow 3 \mathrm{r}+\mathrm{r}+3=154 \mathrm{r}+3=154 \mathrm{r}=15-34 \mathrm{r}=12 \mathrm{r}$ $=3$

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