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Q.
If the total number of selections of at least (n + 1) things from $(2n + 1)$ different things is 256, then the
value of n is
Permutations and Combinations
Solution:
${ }^{(2 n +1)} C _{( n +1)}+{ }^{(2 n +1)} C _{( n +2)}+\ldots \ldots . .+{ }^{(2 n +1)} C _{(2 n +1)}=256 $
$\frac{1}{2}\left[{ }^{(2 n +1)} C _0+{ }^{(2 n +1)} C _1+\ldots \ldots .+{ }^{(2 n +1)} C _{(2 n +1)}\right]=256$
$\frac{1}{2} \cdot 2^{2 n +1}=256 \Rightarrow 2^{2 n }=256=2^8 \Rightarrow n =4 $