If ^ 2n C_2 :^n C_2 = 9:2 and ^n C_r = 10, then r = - Vidyadip

Question

If $^{2n}{C_2}{:^n}{C_2} = 9:2$ and $^n{C_r} = 10$, then $r = $

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Answer

b
(b) $\left( {\frac{{(2n)\;!}}{{2\;!\;(2n - 2)\;!}}} \right)\,\,2 = \left( {\frac{{n\;!}}{{2\;!(n - 2)\;!}}} \right)\,\,9$

$ \Rightarrow (2n)(2n - 1)2 = 9n(n - 1) \Rightarrow n = 5$

Now $^5{C_r} = 10 \Rightarrow r = 2$.

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