If ^n{C_{r - 2}} = 36 , ^n{C_{r - 1}} = 84&nb | vedclass

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Question

$^{\rm{n}}{{\rm{C}}_{{\rm{r}} - 2}} = 36,{\,^{\rm{n}}}{{\rm{C}}_{{\rm{r}} - 1}} = 84,{\,^{\rm{n}}}{{\rm{C}}_{\rm{r}}} = 126$

$\frac{{^n{C_{r - 1}}}

Vedclass · Accepted Answer

$9$

Vedclass · Answer

$^{m{n}}{{m{C}}_{{m{r}} - 2}} = 36,{\,^{m{n}}}{{m{C}}_{{m{r}} - 1}} = 84,{\,^{m{n}}}{{m{C}}_{m{r}}} = 126$

$\frac{{^n{C_{r - 1}}}}{{^n{C_{r - 2}}}} = \frac{{84}}{{36}} \Rightarrow \frac{{{m{n}} - {m{r}} + 2}}{{{m{r}} - 1}} = \frac{7}{3}$

$\Rightarrow 3 \mathrm{n}+13=10 \mathrm{r}$         ....$(1)$

$\frac{{^{m{n}}{C_r}}}{{^n{{m{C}}_{r - 1}}}} = \frac{{126}}{{84}} \Rightarrow \frac{{{m{n}} - {m{r}} + 1}}{{m{r}}} = \frac{3}{2}$

$\Rightarrow 2 \mathrm{n}+2=5 \mathrm{r}$       ......$(2)$

$	herefore \mathrm{n}=9, \mathrm{r}=4$

$^n{C_{r - 1}} = {\,^9}{{m{C}}_8} = 9$

If $^n{C_{r - 2}} = 36$ , $^n{C_{r - 1}} = 84$ and $^n{C_r} = 126$ , then value of $^n{C_{2r}}$ is

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