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  4. The value of 2n [1.3.5...(2n - 3) (2n - 1)] is

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Q. The value of $2^n [1.3.5...(2n - 3) (2n - 1)]$ is

Permutations and Combinations

Solution:

$[1.3.5...... (2n - 1)]2^n$
$=\frac{1.2.3.4.5.6....\left(2n-1\right)\left(2n\right)2^{n}}{2.4.6......2n}=\frac{\left(2n\right)!2^{n}}{2^{n}\left(1.2.3...n\right)}=\frac{\left(2n\right)}{n!}$