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A student is allowed to select at the most n books from a collection of $2n+1$ books. The no. of ways in which he can select at least one book is 63, then $n$ = ?

$\begin{array}{1 1} 1 \\ 2 \\ 3 \\ 4 \end{array} $

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The no. of ways in which one can select at least one book
and at the most $n$ books from $2n+1$ books is
we know
Put $x=1$ and also we know that $^nC_r=^nC_{n-r}$
$i.e.,\:\: 2\big[^{2n+1}C_0+^{2n+1}C_1+....^{2n+1}C_n\big]=2^{2n+1}$
$\Rightarrow\:^{2n+1}C_1+....^{2n+1}C_n=2^{2n}-1$ $(Since\:^{2n+1}C_0=1)$
Given that $^{2n+1}C_1+^{2n+1}C_2+^{2n+1}C_3+...........^{2n+1}C_n=63$
answered Oct 28, 2013 by rvidyagovindarajan_1

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